41. Wolfgang Pauli - Definition Of Wolfgang Pauli By The Free Online Dictionary, The Meaning of wolfgang Pauli. What does wolfgang Pauli mean? wolfgang Pauli synonyms wolfgang Krauser wolfgang KreisslDoerfler wolfgang krull http://www.thefreedictionary.com/Wolfgang Pauli

Domain='thefreedictionary.com' word='Wolfgang Pauli' Your help is needed: American Red Cross The Salvation Army join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia ... encyclopedia Wolfgang Pauli Also found in: Columbia Wikipedia Hutchinson 0.06 sec. Page tools Printer friendly Cite / link Email Feedback Thesaurus Legend: Synonyms Related Words Antonyms Noun Wolfgang Pauli - United States physicist (born in Austria) who proposed the exclusion principle (thus providing a theoretical basis for the periodic table) (1900-1958) Pauli nuclear physicist - a physicist who specializes in nuclear physics Mentioned in References in classic literature No references found No references found Dictionary/thesaurus browser Full browser Wolffian Wolffian body Wolffian duct Wolffiella ... Wolfgang Amadeus Mozart Wolfgang Pauli wolfhound wolfish wolfishly Wolfkin ... Wolfgang K.H. Panofsky

42. Math Forum - Searching For New Mathematics In 1930, German mathematician wolfgang krull reflected on the isolation mathematicianssometimes feel. The more we ourselves are enraptured by the beauties http://mathforum.org/social/articles/ivars.html

Searching For New Mathematics by Ivars Peterson Back to Articles on the Public Understanding of Math Nonmathematicians interested in keeping up with contemporary mathematical research face daunting obstacles. The high level of abstraction, unenlightening notation, and the format of journal papers all conspire to make any foray into the mathematical literature frustrating and unrewarding. Mathematicians can do more to make their research accessible to a wider audience. To most outsiders, modern mathematics represents unknown territory; its borders are protected by dense thickets of technical terms, its landscapes strewn with indecipherable equations and impenetrable concepts. Few realize that the world of modern mathematics is rich with vivid images, potentially useful notions, and provocative ideas. Students of mathematics, faced with the chore of memorizing multiplication tables, lost in the labyrinths of geometric proofs, or pondering how long it takes a slowly leaking conical vessel to drain, often have the feeling that mathematics is little more than an unchanging body of knowledge that must be painstakingly and painfully passed on from generation to generation. Missing is a sense of how mathematics has evolved since its origins in the distant past and how new mathematics is constantly being discovered and created. Even scientists and engineers often harbor an image of mathematics as a well-stocked warehouse from which to select ready-to-use formulas, theorems, and results to advance their own theories. Mathematicians, on the other hand, see their field as a rapidly growing endeavor, furnishing a rich and ever-changing variety of abstract notions.

43. People Whose Names Are Embedded In Math Subject Classifcation (German) wolfgang Franz in memoriam Jahresber. Deutsch. Math.Verein. Oystein (1899-1971) krull, wolfgang (1899-1980) Grobner, wolfgang (1900-1967) http://www.math.niu.edu/~rusin/known-math/98/MSC.names

Date: Sun, 6 Jun 1999 12:40:49 +0200 From: "Yuri I. Manin" Date: Thu, 28 Mar 2002 12:43:10 -0800 From: "Antreas P. Hatzipolakis" Cc: rusin@math.niu.edu, a_arakelov@yahoo.co.uk To: hyacinthos@yahoogroups.com Subject: Suren Arekelov This list is devoted to Triangle Geometry. However, from time to time, will be allowed discussions on themes of general interest. Especially when the geometric traffic is not too much. (like this day). Some time ago I asked for information (in fact I FWD-ed an e-mail of D. Rusin) about a notable mathematician who disappeared from the math. horizon. The mathematician is the algebraic geometer Suren Arakelov. Andrei Arakelov has kindly sent the following: > > Date: Thu, 28 Mar 2002 11:29:55 +0000 (GMT) > From: Andrei Arakelov > Subject: Suren Arakelov > To: Antreas P. Hatzipolakis Date: Sat, 05 Feb 2005 11:35:53 +0000 Message-ID:

44. Manuscripts About the same time wolfgang krull gave a more general, universal definition ofvaluation which turned out to be applicable also in many other mathematical http://www.rzuser.uni-heidelberg.de/~ci3/manu.html

32 Manuscripts by Peter Roquette (supported in part by the Deutsche Forschungsgemeinschaft for downloading as ps-file, or dvi-file, or pdf-file (Last modified: Apr 29, 2005) to homepage Contents: Mar 9, 2005 From FLT to finite groups. The remarkable career of Otto Grün. Jan 21, 2005 Laudatio für B. H. Matzat Nov 04, 2004 Introduction of Langlands at Arf Lecture Feb 28, 2004 The Brauer-Hasse-Noether theorem in historical perspective Aug 27, 2003 On the embedding problem for global fields July 03, 2003 The Riemann hypothesis in characteristic p, its origin and development. Part 2 July 02, 2003 The Riemann hypothesis in characteristic p, its origin and development. Part 1 Feb 13, 2003 Erinnerungen an Helmut Hasse in Berlin (5. Mai 1997) Jan 09, 2003 Reminiscences of Arnold Ross Sep 30, 2002 May 26, 2002 Zum Fermat-Problem (24.1.1998) Apr 16, 2002 Helmut Hasse in Halle Mar 25, 2002 David Hilbert (1862-1943). Zum 140. Geburtstag Mar 08, 2002 Mar 12, 2002

45. NEWSLETTER ARCHIVE 1999 anniversaries Felix Klein, Sophus Lie and wolfgang krull, 12. Letters, 14.Societies Finnish Mathematical Society, 16 http://emis.math.ecnu.edu.cn/newsletter/archive_contents.html

46. 510(k)s Final Decisions Rendered For May 2005 ATTN wolfgang krull PHONE NO 978952-2900 300 FOSTER STREET SE DECISION MADE05-MAY-05 LITTLETON, MA 01460 510(k) SUMMARY AVAILABLE FROM FDA THIRD PARTY http://www.fda.gov/cdrh/510k/summay05.html

FDA Home Page CDRH Home Page Search CDRH A-Z Index ... Contact CDRH 510(k)s Final Decisions Rendered for May 2005 Some of the documents on this section of the CDRH Website are available only in PDF format and may not be accessible to those with certain disabilities. If you cannot access the documents you are interested in, please use the accessibility link for assistance. SUBMITTER ADDRESS LISTING FOR CDRH SUBSTANTIALLY EQUIVALENT (SE) 510(K) SUMMARIES OR 510(K) STATEMENTS FOR FINAL DECISIONS RENDERED DURING THE PERIOD 01-MAY-2005 THROUGH 31-MAY-2005 DEVICE: XPERT SELF-EXPANDING TRANSHEPATIC BILIARY STENT SYSTEM ABBOTT LABORATORIES 510(k) NO: (SPECIAL) ATTN: JOANNA DEVELTER PHONE NO : 650-474-3331 400 SAGINAW DRIVE SE DECISION MADE: 20-MAY-05 REDWOOD CITY, CA 94063 510(k) SUMMARY AVAILABLE FROM FDA DEVICE: PRECISION XTRA PLUS OR OPTIUM PLUS, BLOOD GLUCOSE TEST STRIPS ABBOTT LABORATORIES INC 510(k) NO: (SPECIAL) ATTN: ANDREA RUTH PHONE NO : 510-749-6343 1360 SOUTH LOOP ROAD SE DECISION MADE: 27-MAY-05 ALAMEDA, CA 94502 510(k) SUMMARY AVAILABLE FROM FDA DEVICE: ACON +/- MIDSTREAM PREGNANCY TEST ACON LABORATORIES, INC. 510(k) NO:

47. Germaine Krull - Exhibitions Germaine krull. FAPh. Nov 20 Dec 24,2004 Walker Evans , wolfgang Tillmans ,Brassaï , Germaine krull , Albert Renger-Patzsch , UMBO , Seamus Nicolson http://www.photography-now.com/artists/K07272.html

All Countries Albania Argentina Australia Austria Belgium Brazil Canada Chile China Croatia Cuba Czech Republic Denmark Estonia Finland France Germany Great Britain Greece Hungary Iceland Ireland Israel Italy Japan Liechtenstein Lithuania Luxembourg Malaysia Mali Mexico Netherlands New Zealand Norway Poland Portugal Romania Russia Serb/Mont Singapore Slovakia Slovenia South Africa South Korea Spain Sweden Switzerland Taiwan Thailand Turkey USA USA Japan Germany Australia ... China Germaine Krull * 1897-1985 Germany Exhibitions Events Publications Bruce Silverstein Gallery 504 West 22nd Street, NY 10011 New York NewYork, USA Phone: +1-212.6273930 Tue-Sat 11-18 Germaine Krull FAPh Nov 20 - Dec 24,2004 Stiftung Fotografie und Kunstwissenschaft Germany Phone: 0221.3980716 Tue-Fri 14-18, Sat 12-16 Germaine Krull FAPh Dec 06 - Apr 30,2004 Group exhibitions Sprengel Museum Hannover Kurt-Schwitters-Platz, 30169 Hannover Germany Phone: 0511.16843875 Tue 10-20, Wed-Sun 10-18 Heidi Specker Germaine Krull CPh Oct 09 - Jun 26,2006 Sprengel Museum Hannover Kurt-Schwitters-Platz, 30169 Hannover Germany Phone: 0511.16843875

48. Algebraic Geometry - Wikipedia, The Free Encyclopedia rings and their ideals) had been and was being developed by David Hilbert,Max Noether?, Emanuel Lasker, Emmy Noether, wolfgang krull?, and others. http://www.xahlee.org/_p/wiki/Algebraic_geometry.html

Algebraic geometry From Wikipedia, the free encyclopedia. Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra , especially commutative algebra , with geometry . It can be seen as the study of solution sets of systems of algebraic equations . When there is more than one variable, geometric considerations enter, and are important to understand the phenomenon. One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique. Table of contents show hide 1 Zeroes of simultaneous polynomials 2 Affine varieties ... edit Zeroes of simultaneous polynomials In classical algebraic geometry, the main objects of interest are the vanishing sets of collections of polynomials , meaning the set of all points that simultaneously satisfy one or more polynomial equations. For instance, the two-dimensional sphere in three-dimensional Euclidean space R could be defined as the set of all points ( x y z ) with x y z A "slanted" circle in R can be defined as the set of all points ( x y z ) which satisfy the two polynomial equations x y z x y z edit Affine varieties First we start with a field k . In classical algebraic geometry, this field was always

49. Third Grade - Music - Lesson 11 - Alphabet Canon of lively dialog that brings wolfgang and his family to life. krull, Kathleen . krull has written a lighthearted, upbeat version of the lives of 20 http://www.cstone.net/~bcp/3/3FMusic.htm

Third Grade - Music - Lesson 11 - Alphabet Canon Objectives Recall the names of lines and spaces in music notation. Sing an alphabet song in unison. Recognize the tune as that of "Twinkle, Twinkle, Little Star." Identify meter signature, quarter, half, and eighth notes. Hear a definition of the musical term canon Sing the alphabet song in canon. Materials Music for "The Alphabet," to be used for transparency (attached) (You will find the song written out for 2 groups in canon form so the students can see exactly what is going on musically. Generally, musicians would simply write the number 1 above the first note of the first measure and number 2 above the first note of the second measure, but that is a convention not at all familiar to these students, since they have not sung any other rounds or canons before this one.) Procedure Tell the class they are going to learn an alphabet song, based on an old familiar tune they will probably recognize from when they were little children. It will be easy for them to sing the tune, or melody, because it sounds so familiar to their ears, but this time they will be singing it and also seeing it written out in music notation. Say to them: I am going to begin singing this melody, and you can join in whenever you recognize the tune from your musical memories. Begin the tune (for "Twinkle, Twinkle, Little Star"), simply singing it on the syllable "la" and encouraging the students to join in as they will; you may need to sing it through a few times before everyone has joined. Ask the students: What is the name of that tune? ("Twinkle, Twinkle, Little Star")

50. List Of Scientists By Field Translate this page krull, wolfgang. Krünig, August Karl. Krutkov, Iurii Aleksandrovich. Krylov,Aleksei Nikolaevich. Krylov, Aleksei Nikolaevich. Krylov, Nikolai Mitrofanovich http://www.indiana.edu/~newdsb/k.html

Kablukov, Ivan Alexsevich Kaempfer, Engelbert Kaempfer, Engelbert Kaestner, Abraham Gotthelf Kagan, Benjamin Fedorovich Kahlenberg, Louis Albrecht Kaiser, Frederik Kalm, Pehr Kaluza, Theodor Franz Eduard Kaluza, Theodor Franz Eduard Kamerlingh Onnes, Heike Kanaka Kane, Robert John Kant, Immanuel Kapteyn, Jacobus Cornelius Kargin, Valentin Alekseevich Karpechenko, Georgii Dmitrievich Karpinski, Louis Charles Karpinski, Louis Charles Karpinsky, Alexandr Petrovich Karrer, Paul Karsten, Karl Johann Bernhard Karsten, Karl Johann Bernhard Kater, Henry Kaufmann, Walter Kavraysky, Vladimir Vladimirovich Kavraysky, Vladimir Vladimirovich Kavraysky, Vladimir Vladimirovich Kay, George Frederick Kay, Marshall Kayser, Heinrich Johannes Gustav Keckermann, Bartholomew Keckermann, Bartholomew Keckermann, Bartholomew Keeler, James Edward Keesom, Willem Hendrik Keilin, David Keilin, David Keilin, David Keill, James Keill, James Keill, John Keill, John Keir, James Keith, Arthur Keith, Arthur Keith, Arthur Kekule von Stradonitz, August Kellner, David Kellner, David Kellogg, Albert

51. New Dictionary Of Scientific Biography Translate this page krull, wolfgang Krylov, Aleksei Nikolaevich Krylov, Nikolai Mitrofanovich Kummer,Ernst Eduard Kuratowski, Kazimierz Kürschák, József http://www.indiana.edu/~newdsb/math.html

Make Suggestions Mathematics Abel, Niels Henrik Abraham Bar ?iyya Ha-Nasi Abu Kamil Shuja? Ibn Aslam Ibn Mu?ammad Ibn Shuja? Abu'l-Wafa? al-Buzjani, Mu?ammad Ibn Mu?ammad Ibn Ya?ya Ibn Isma?il Ibn al- ?Abbas Adams, John Couch Adelard of Bath Adrain, Robert Aepinus, Franz Ulrich Theodosius Agnesi, Maria Gaetana Aguilon, François d' A?mad Ibn Yusuf Aida Yasuaki Ajima Naonobu Akhiezer, Naum Il'ich Albert, Abraham Adrian Albert of Saxony Alberti, Leone Battista Aleksandrov, Pavel Sergeevich Alembert, Jean Le Rond d' Alzate y Ramírez, José Antonio Ampère, André-Marie Amsler, Jakob Anatolius of Alexandria Anderson, Oskar Johann Viktor Andoyer, Henri Angeli, Stefano Degli Anthemius of Tralles Antiphon Apollonius of Perga Appell, Paul Arbogast, Louis François Antoine Arbuthnot, John Archimedes Archytas of Tarentum Argand, Jean Robert Aristaeus Aristarchus of Samos Arnauld, Antoine Aronhold, Siegfried Heinrich Artin, Emil Atwood, George Autolycus of Pitane Auzout, Adrien

52. Wolfgang Krull Université Montpellier II Translate this page wolfgang krull (1899-1971). Cette image et la biographie complète en anglaisrésident sur le site de l’université de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1403

53. Die FOTOGRAFISCHE SAMMLUNG Translate this page Sie umfaßt heute über 50.000 Fotografien und mehrere Nachlässe, unter anderemvon Helma Lerski, Germaine krull, wolfgang Weber, Walter Peterhans, http://www.museum-folkwang.de/wirfot.htm

Die FOTOGRAFISCHE SAMMLUNG Die FOTOGRAFISCHE SAMMLUNG im Museum Folkwang existiert als selbständige Abteilung des Museums seit 1979. Seither ist die Sammlung systematisch ergänzt und erweitert worden. Sie umfaßt heute über 50.000 Fotografien und mehrere Nachlässe, unter anderem von Helma Lerski, Germaine Krull, Wolfgang Weber, Walter Peterhans, Otto Steinert und die Archive von Peter Keetman und ringl + pit. Außerdem sind große Werkgruppen von David Octavius Hill/Robert Adamson, Heinrich Kühn, Hugo Erfurth, Lázló Moholy-Nagy, Albert Renger-Patzsch, August Sander und Edward Steichen Teil dieser Sammlung. Der Schwerpunkt der Sammlung liegt im 20. Jahrhundert; aber auch zum 19. Jahrhundert enthält sie herausragende Bildleistungen, speziell zur Porträt-, Architektur-, und Landschaftsdarstellung. Die Sammlung ist international orientiert mit besonderer Konzentration auf die Zwanziger Jahre, die Nachkriegszeit und auf zeitgenössischen Arbeiten: Thematisch liegt ihr Schwerpunkt auf der Porträt- und Architekturfotografie, der Geschichte der Bildberichterstattung und der künstlerischen Fotografie, sowie Konvolute zu Fotoform, Subjektive Fotografie, Steinert und Schüler. Öffnungszeit zur Einsicht der Bestände: Donnerstag 11.00 bis 13.00 Uhr und 14.00 bis 17.00 Uhr

54. Art In America: Wols's Haunted Kitchen - Alfred Otto Wolfgang Schulze, Photograp Full text of the article, Wols s Haunted Kitchen Alfred Otto wolfgang Schulze, Her book Germaine krull Photographer of Modernity has recently been http://www.findarticles.com/p/articles/mi_m1248/is_1_88/ai_58616904

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Advanced Search Home Help IN free articles only all articles this publication Automotive Sports 10,000,000 articles - not found on any other search engine. FindArticles Art in America Jan 2000 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Related Searches Photographers / Exhibitions Harvard University. Busch-Reisinger Museum / Exhibitions Featured Titles for ALAN Review Afterimage American Drama American Music Teacher ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports Wols's Haunted Kitchen - Alfred Otto Wolfgang Schulze, photographer Art in America Jan, 2000 by Kim Sichel Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. Bauhaus precision and a Surrealist taste for the uncanny meet in the domestic still lifes of the German artist Wols, whose photographs were recently on view at Harvard. As a painter, Wols is known primarily as the European counterpart to Jackson Pollock; both artists occupy mythic positions heralding the transition from Surrealist-inspired imagery to gestural abstraction. Arriving in Paris from Dresden in 1932, at age 19, Wols made imaginative and delicately macabre watercolors and pen-and-ink drawings. He had already begun to practice photography as well; in Paris he tried to earn a living as a photographic portraitist, continuing with the medium until around 1942. His drawings of the 1930s belong to the same family of Surrealist dream imagery as those of Yves Tanguy, Andre Masson and Max Ernst. During these years Wols incorporated gentle yet disturbing cityscapes and oddly detailed narrative images into his work. His drawings gradually turned away from representational imagery, and his first paintings, begun in 1946, incorporate gestural marks, scratches and rough textures.

55. Photographie - Historicum.net Translate this page Sie beinhaltet mehrere Nachlässe, unter anderem von Helma Lerski, Germaine krull,wolfgang Weber, Walter Peterhans, Otto Steinert und die Archive von Peter http://www.photographie.historicum.net/archive-deu.html

historicum.net Fachgebiete Photographie : Archive Startseite Redaktion Call for Papers / Tagungen Archive / Sammlungen ... Zeitschriften Archive / Sammlungen Archive und Sammlungen in Deutschland www.bauhaus.de/sammlungen/fotografie.htm BAUHAUS-ARCHIV FOTOGRAFIE BERLIN www.berlinischegalerie.de BERLINISCHE GALERIE - DIE PHOTOGRAPHISCHE SAMMLUNG BERLIN Die Berlinische Galerie hat von der J. Paul Getty Stiftung Adresse: Berlinische Galerie - Die Photographische Sammlung, Mathfesselstr. 28-48, D-10965 Berlin, Tel: 030 - 78902600, Fax: 030 - 78902701 www.smb.spk-berlin.de/smb/de/sammlungen HELMUT NEWTON STIFTUNG BERLIN http://userpage.fu-berlin.de/~chelone/institut/abgudia.htm Parallel zur Abguss-Sammlung Antiker Plastik wird seit 1977 am Institut für Klassische Archäologie an der Freien Universität Berlin - ebenfalls mit dem Schwerpunkt "Antike Plastik" - eine Fotothek (etwa 60.000 aufgezogene Fotos in Kästen) und eine Diathek (etwa 110.000 Groß-und Kleindias) aufgebaut. Die Website gibt keine weiterführenden Auskünfte; 2004 wurde eine Publikation über die Sammlung veröffentlicht: Annetta Alexandridis und Wolf-Dieter Heilmeyer, Archäologie der Photographie - Bilder aus der Photothek der Antikensammlung Berlin. http://www.smb.spk-berlin.de/kb/s.html

56. Theater Wiwo - Schauspiel Und Puppenspiel - Lesetheater Translate this page Bekenntnisse des Hochstaplers Felix krull/Romanfragment von Thomas Mann. NEUWilmi und wolfgang Gerber lesen Märchen von starken Frauen http://www.theaterwiwo.de/Programme/Lesungen/lesungen.html

Home Programme Presse Termine ... Puppenspiele Übersicht über die Schauspiele und Lesungen NEU: Märchen von starken Frauen literarisch-musikalischer Salon Wo Liebe nicht ist, sprich das Wort nicht aus/Johannes Bobrowski Leiden und Kämpfen sind die Organe des Werdens/Ernst Barlach ... Bekenntnisse des Hochstaplers Felix Krull/Romanfragment von Thomas Mann NEU: Wilmi und Wolfgang Gerber lesen: Märchen v on starken Frauen Eine vergnügliche Zwiesprache in Augenhöhe Im täglichen Leben kennen wir sie alle, und wen wundert es da, wenn sie im Reich der Märchen neu entdeckt werden: die starken Frauen. Wi und Wo unternehmen mit ihrem Märchenabend eine Reise durch viele Kontinente und begegnen klugen, mutigen, warmherzigen und selbstbewussten Frauen. Dass dabei nicht ein altes Klischee durch ein neues ersetzt wird, dafür sorgt eine kleine Überraschung. Für Menschen fast jeden Alters. Dauer: ca. 70 Min. [ zurück W O LIEBE NICHT IST, SPRICH DAS WORT NICHT AUS Gedichte und Prosa von JOHANNES BOBROWSKI (1917 - 1965) szenisch dargestellt von Wilmi und Wolfgang Gerber, Leipzig

57. @article {MR8499g, AUTHOR = {Zariski, Oscar}, TITLE = {A New @inproceedings {MR13526c, AUTHOR = {krull, wolfgang}, TITLE = {Jacobsonsches {R}adikalund {H}ilbertscher {N}ullstellensatz}, BOOKTITLE = {Proceedings http://www.math.uiuc.edu/~dan/Courses/2003/Fall/248/sample/sample.bib

58. 3518 M. Atiyah/I. MacDonald Introduzione All Algebra Commutativa 2025 wolfgang krull Idealtheorie. Springer 1968. 1506 Ernst Kunz Einfuehrungin die kommutative Algebra und algebraische Geometrie. Vieweg 1980. http://felix.unife.it/Root/d-Mathematics/d-Algebraic-geometry/b-Commutative-alge

3518 M. Atiyah/I. MacDonald: Introduzione all'algebra commutativa. Feltrinelli 1981. S. Balczerzyk/T. Jozefiak: Commutative Noetherian and Krull rings. Horwood 1989, 210p. Pds. 35. First part of a two-volume treatise. S. Balczerzyk/T. Jozefiak: Commutative rings. Dimension, multiplicity and homological methods. Horwood 1989, 200p. Pds. 35. Together with "Commutative Noetherian and Krull rings" a good and complete introduction the local algebra for algebraic geometry. C. Berenstein/R. Gay/A. Vidras/A. Yger: Residue currents and Bezout identities. Birkhaeuser 1993, 180p. 3-7643-2945-9. DM 72. 3329 Nicolas Bourbaki: Commutative algebra. Chapters 1-7. Springer 1989. William Brown: Matrices over commutative rings. Dekker 1993, 300p. $ 115. 1224 Rainer Brüske/Friedrich Ischebeck/Ferdinand Vogel: Kommutative Algebra. Bibl. Inst. 1989. Winfried Bruns/J. Herzog: Cohen-Macaulay rings. Cambridge UP 1993, 415p. 0-521-41068-1. Pds. 45. 2807 Winfried Bruns/Aron Simis (ed.): Commutative algebra. SLN Math. 1430 (1990). Y. Diers: Categories of commutative algebras. Oxford UP 1992. 4687 Jean Dieudonne': Topics in local algebra. Univ. Notre Dame Press 1967. 11998 David Eisenbud: Commutative algebra with a view toward algebraic geometry. Springer 1995, 790p. $45. 8362 Mark Green: Review of Eisenbud's "Commutative algebra wiht a view toward algebraic geometry". Bull. AMS 33 (1996), 367-370. 16045 Gert-Martin Greuel/Gerhard Pfister: A SINGULAR introduction to commutative algebra. Springer 2002, 600p. Eur 43. 1472 Wolfgang Groebner: Algebraische Geometrie. 2 volumes. Bibl. Inst. 1968. 2716 Craig Huneke: An algebraist commuting in Berkeley. Math. Intell. 11/1 (1989), 40-52. 2603 M.-P. Malliavin: Algebre commutative. Masson 1985. Very clear. Especially good as a foundation for algebraic number theory. Marco Fontana/Francesco Pappalardi: The prime spaces as spectral spaces. Annali mat. pura e appl. 160 (1991), 331-345. Robert Gilmer/William Heinzer: Products of commutative rings andzero-dimensionality. Trans. AMS 331 (1992), 663-680. 3457 Melvin Hochster/Craig Huneke/Judith Sally (ed.): Commutative algebra. Springer 1989. Craig Huneke/Bernd Ulrich/Wolmer Vasconcelos: On the structure of certain normal ideals. Compos. Math. 84 (1992), 25-42. Introduces the notion of residual linkage. Irving Kaplansky: Projective modules. Ann. Math. 68 (1958), 372-377. Irving Kaplansky: Commutative rings. Chicago UP 1970. M.-A. Knus: Quadratic and hermitian forms over rings. Springer 1991, 520p. DM 198. 2025 Wolfgang Krull: Idealtheorie. Springer 1968. 1506 Ernst Kunz: Einfuehrung in die kommutative Algebra und algebraische Geometrie. Vieweg 1980. 16282 Ernst Kunz: Introduction to commutative algebra and algebraic geometry. Birkhäuser 1985, 230p. $60. Translation of 1506. 2815 Herbert Kurke/G. Pfister/M. Roczen: Henselsche Ringe und algebraische Geometrie. Berlin 1975. F. Macaulay: The algebraic theory of modular systems. Cambridge UP 1994, 150p. 0-521-45562-6 (pb). $20. 2460 Hideyuki Matsumura: Commutative ring theory. Cambridge UP 2002, 320p. $38. Ezra Miller/Bernd Sturmfels: Combinatorial commutative algebra. Springer 2005, 430p. $50. Ezra Miller/Bernd Sturmfels/Kohji Yanagawa: Generic and cogeneric monomial ideals. J. Symb. Comp. 29/4-5 (2000), 691-708. Masayoshi Nagata: Local rings. Interscience 1962, 230p. 4688 Douglas Northcott: Ideal theory. Cambridge UP 1953. Christian Peskine: An algebraic introduction to complex projective geometry I. Commutative algebra. Cambridge UP 1996, 240p. 0-521-48072-8. Pds. 25. 16215 Miles Reid: Undergraduate commutative algebra. Cambridge UP 1995, 150p. $18. 5745 Heinrich Reitberger: Stellenringe. 5738 Laugwitz, 155-175. 1491 Bodo Renschuch: Elementare und praktische Idealtheorie. Berlin 1976. J. Ruiz: The basic theory of power series. Vieweg 1993, 130p. 3-528-06525-9. DM 36. Basic power series techniques used in analytic and algebraic geometry. Nullstellensaetze, Artin's approximation theorem, Zariski's main theorem. 1589 Guenter Scheja/Uwe Storch: Lehrbuch der Algebra. 3 volumes. Teubner 1980. Jean-Pierre Serre: Local algebra. Springer 2000, 110p. Eur 60. Translation of the SLN-booklet. Wolmer Vasconcelos: Arithmetic of Blowup Algebras. Cambridge UP 1994, 330p. 0-521-45484-0. $34.95 1590 B. van der Waerden: Algebra. 2 volumes. Springer 1966. 3131 Oscar Zariski/Pierre Samuel: Commutative algebra. 2 volumes. Springer 1986.

59. AMCA: Differences In Sets Of Lengths By Wolfgang A. Schmid wolfgang A. Schmid University of Graz. Let H be a krull monoid with finite classgroup G (eg the multiplicative semigroup of the ring of integers of some http://at.yorku.ca/c/a/k/l/29.htm

Atlas Mathematical Conference Abstracts Conferences Abstracts Organizers ... About AMCA Journées Arithmétiques XXIII July 6-12, 2003 University of Graz and University of Technology of Graz Graz, Styria, Austria Organizers S. Frisch, A. Geroldinger, P. Grabner, F. Halter-Koch, C. Heuberger, G. Lettl, R. Tichy View Abstracts Conference Homepage Differences in Sets of Lengths by Wolfgang A. Schmid University of Graz Let H be a Krull monoid with finite class group G (e.g. the multiplicative semi-group of the ring of integers of some algebraic number field) and a in H not a unit. If a=u ... u k with atoms u i in H, then k is called the length of the factorization and L in N denotes the set of lengths of a. Sets of lengths are generalized arithmetical progressions. In this talk we present results on possible differences in these generalized arithmetical progressions. Moreover we will use these results to obtain information on the class group via the system of sets of length. The crucial tool in our investigations will be the blockmonoid generated by G. Date received: April 28, 2003

60. AMCA: Weakly Half-factorial Subsets Of Finite Abelian Groups And Arithmetical Ap wolfgang A. Schmid KarlFranzens-Universität Graz, Austria For a krull monoidthe problem of deciding whether the monoid is half-factorial can be http://at.yorku.ca/cgi-bin/amca/caqi-61

Atlas Mathematical Conference Abstracts Conferences Abstracts Organizers ... About AMCA Joint Meeting of AMS, DMV, and ÖMG June 16-19, 2005 Johannes Gutenberg University Mainz, Germany Organizers Volker Bach, Mainz; Klaus D. Bierstedt, DMV; Susan Friedlander, Associate Secretary, AMS View Abstracts Conference Homepage Weakly half-factorial subsets of finite abelian groups and arithmetical applications by Wolfgang A. Schmid Karl-Franzens-Universität Graz, Austria Coauthors: An atomic monoid H is called half-factorial if for every element a H all factorizations of a into atoms (irreducible elements) have the same lengths. A subset G G of an abelian group is called a half-factorial set if the block monoid B (G ), the monoid of zero-sum sequences in G , is a half-factorial monoid. For a Krull monoid the problem of deciding whether the monoid is half-factorial can be transferred to the problem of deciding whether the set of classes containing primes is a half-factorial subset of the class group. In case G is a finite abelian group, it is well-known that a subset G G is half-factorial if and only if the cross number (a weighted length) of each minimal zero-sum sequence in G G is called weakly half-factorial if the cross number of each minimal zero-sum sequence in G is a positive integer.

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