1. The Mathematics Genealogy Project - Wolfgang Krull Wolfgang Krull Biography. Ph.D. AlbertLudwigs-Universit t Freiburg im Breisgau 1922 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Poster Of Krull Wolfgang Krull. lived from 1899 to 1971. Wolfgang Krull proved the KrullSchmidttheorem for decomposing abelian groups and defined the Krull dimension of a http://www-groups.dcs.st-and.ac.uk/~history/Posters2/Krull.html

Wolfgang Krull lived from 1899 to 1971 Wolfgang Krull proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring. Find out more at http://www-history.mcs.st-andrews.ac.uk/history/ Mathematicians/Krull.html

3. Wolfgang Krucker - Wirtschaftssteuerung In Westdeutschland 1945 Gesammelte Abhandlungen Wolfgang Krull Paulo Ribenboim Gesammelte Abhandlungen Wolfgang Wolfgeng Wolvgang Wolvgeng Worfgang Worfgeng http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Gesammelte Abhandlungen Collected Papers By Wolfgang Krull Paulo Gesammelte Abhandlungen Collected Papers by Wolfgang Krull br Paulo Ribenboim br Direct Textbook Price Comparison http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Wolfgang Krull / Collected Papers - Compare Prices Wolfgang Krull / Collected Papers Sales Rank 999999 Customer rating 0.00 Released Aug 1, 1999 Manufacturer Walter de Gruyter http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Wolfgang Krull - Definition Of Wolfgang Krull In Encyclopedia Wolfgang Krull (1899 1971) was a German mathematician, after whom Krull dimension, the Krull topology, and Krull's principal ideal theorem are http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Wolfgang Krull - Definition Of Wolfgang Krull In Encyclopedia Wolfgang Krull (1899 1971) was a German mathematician, after whom Krull dimension,the Krull topology, and Krull s principal ideal theorem are named. http://encyclopedia.laborlawtalk.com/Wolfgang_Krull

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law Wolfgang Krull (1899 - 1971) was a German mathematician, after whom Krull dimension , the Krull topology , and Krull's principal ideal theorem are named. This article is a stub . You can help Wikipedia by expanding it This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article "Wolfgang_Krull" Browse Wolfgang Amadeus Mozart wolf's milk Wolfgang Krull wolfsbane ... Wollaston Search Word: General Encyclopedia Legal Medical Computer Science Law Forum Embed a dictionary search in your own web page Link to Us Advertise Add to Favorites ... Legal notices

8. BookkooB Wolfgang Krull / Collected Papers - Wolfgang Krull This page lets you compare prices for Wolfgang Krull / Collected Papers by Wolfgang Krull from the leading UK book stores in seconds and save money http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Wolfgang Krull Wolfgang Krull (1899 1971) was a German mathematician, working in the field ofcommutative algebra. See Krull dimension, the Krull topology, http://www.algebra.com/algebra/about/history/Wolfgang-Krull.wikipedia

Wolfgang Krull Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc Wikimedia needs your help in its 21-day fund drive. See our fundraising page You did it! Nearly US$220,000 has been raised . Thank you for your generosity! Wolfgang Krull Wolfgang Krull ) was a German mathematician, working in the field of commutative algebra See: Krull dimension , the Krull topology Krull's intersection theorem and Krull's principal ideal theorem This biographical article about a mathematician is a stub . You can help Wikipedia by expanding it Retrieved from " http://en.wikipedia.org/wiki/Wolfgang_Krull Categories Mathematician stubs 1899 births ... German mathematicians Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link In other languages Deutsch This page was last modified 18:18, 12 August 2005. All text is available under the terms of the GNU Free Documentation License (see for details).

10. Definition/Research - Wiki/Wolfgang_Krull Wolfgang Krull (1899 1971) was a German mathematician, after whom Krull dimensionIn commutative algebra, the Krull dimension of a ring R, named http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Wolfgang_Krull - Investigacion Espanola Wolfgang Krull (1899 1971) era matem tico alem n, despu s de que se nombran la dimensi n de Krull, la topolog a de Krull, y el http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Wolfgang Krull - Wikipedia Krull, Wolfgang. ALTERNATIVNAMEN. KURZBESCHREIBUNG, Mathematiker http://de.wikipedia.org/wiki/Wolfgang_Krull

Wikimedia braucht Ihre Hilfe Helfen Sie uns, 200.000$ zu sammeln, damit Wikipedia und ihre Schwesterprojekte auch weiterhin kostenlos und werbefrei der Allgemeinheit zur Verf¼gung stehen. Weitere Informationen auf unserer Spenden-Seite Wolfgang Krull aus Wikipedia, der freien Enzyklop¤die Wolfgang Krull 26. August in Baden-Baden 12. April in Bonn ) war ein deutscher Mathematiker. Sein Schwerpunkt war die Algebra Ideal (Ringtheorie) Er war zun¤chst Sch¼ler von Felix Klein in G¶ttingen und war ganz besonders gepr¤gt von der Zusammenarbeit mit Emmy Noether . Krull wurde 1939 Nachfolger von Otto Toeplitz in Bonn, der schon 1933 wegen der Rassegesetze der Nazis beurlaubt wurde. Nach Krull sind die Krulldimension , Krulltopologie und Krulls Hauptidealsatz benannt. Bearbeiten Weblinks Literatur von und ¼ber Wolfgang Krull im Katalog der DDB Personendaten NAME Krull, Wolfgang ALTERNATIVNAMEN KURZBESCHREIBUNG Mathematiker; Algebraiker Ideal (Ringtheorie) GEBURTSDATUM 26. August GEBURTSORT Kassel STERBEDATUM 12. April STERBEORT Bonn Von " http://de.wikipedia.org/wiki/Wolfgang_Krull

13. Rockland County, NY Naturalization Records Index - Kovach To KRULL BIRGIT 61 19750318 P7306 PR GERMANY KRULL GERHARD 59 19740124 P6967 PRGERMANY KRULL INGE 59 19740124 P6968 PR GERMANY krull wolfgang 59 19740124 http://ftp.rootsweb.com/pub/usgenweb/ny/rockland/court/naturalizations/nats-kl.t

14. SÜDTIROL MARATHON ALTO ADIGE 422.68; 1355 krull wolfgang 38 GER 148 29 422.94; 1304 NORZI Giovanni http://www.runtheplanet.com/sudtirol.htm

VERSIONE ITALIANA DEUTSCHE VERSION ENGLISH VERSION RISULTATI / RESULTS Percorso Luogo - Egna, provincia di Bolzano, si trova a circa venti chilometri a sud di Bolzano, uscita autostrada Egna/Ora. Data - 2 aprile 2000. Orario di partenza - Maratona: ore 8,30; mezza maratona: ore 10. Organizzazione Informazioni e iscrizioni suedt.marathon@rolmail.net Quota di partecipazione - Maratona L. 50.000; mezza maratona L. 25.000. Chiusura iscrizioni il 1 aprile 2000. Iscrizioni oltre il termine: maratona L. 100.000; mezza maratona L. 50.000. Il pagamento deve essere effettuato al ritiro del pettorale. Prenotazioni alberghiere - Igna's Tour, tel. 0471.813.135, fax 0471.823.434. Record del percorso - Maratona: Paul Tangus (Kenia) 2:14.21, Zhulyeva Galina (Ukraina) 2:37.39; mezza maratona: Joseph Kariuki (Kenia) 1:02.51, Rosanna Munerotto (Italia) 1:14.20. Tempo massimo - Maratona: 5 ore; mezza maratona: 2 ore e 30 minuti. Strecke Ort Datum - 2. April 2000. Startzeit - Marathon 8.30 Uhr; Halbmarathon 10.00 Uhr. Organisation Informationen/Einschreibungen suedt.marathon@rolmail.net

15. Krull Biography of wolfgang krull (18991971) wolfgang krull s father was Helmuthkrull and his mother was Adele Siefert krull. Helmuth krull had a dentist s http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Krull.html

Wolfgang Krull Born: 26 Aug 1899 in Baden-Baden, Germany Died: 12 April 1971 in Bonn, Germany Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Wolfgang Krull 's father was Helmuth Krull and his mother was Adele Siefert Krull. Helmuth Krull had a dentist's practice in Baden-Baden and it was in that town that Krull attended school. Klein but was most influenced by Emmy Noether . He attended Klein 's seminar in the session 1920-21 and he then returned to Freiburg and presented his doctoral thesis on the theory of elementary divisors in 1922. Ring theory results from this thesis have recently been found important in the area of coding theory. Appointed as an instructor at Freiburg on 1 October 1922 he was promoted to extraordinary professor in 1926. He remained there until 1928 when he moved to Erlangen. His inaugural address on becoming a full professor at Erlangen was one which says much of how Krull saw mathematics. He saw the role of a mathematician as [1] (see also [2] and [4]):- ... not merely ... finding theorems and proving them. He wants to arrange and group these theorems together in such a way that they appear not only as correct but also as imperative and self-evident. To my mind such an aspiration is an aesthetic one and not one based on theoretical cognition If Emmy Noether had the greatest influence on the topics which Krull would spend his life researching, it can be seen from this inaugural address that it was

16. The Valuation Theory Home Page: Collected Papers By Wolfgang Krull Collected Papers by wolfgang krull now available. krull, wolfgang GesammelteAbhandlungen / Collected Papers Edited by Paulo Ribenboim. http://math.usask.ca/fvk/krull.htm

The Valuation Theory Home Page Collected Papers by Wolfgang Krull now available Krull, Wolfgang Gesammelte Abhandlungen / Collected Papers Edited by Paulo Ribenboim. Published by de Gruyter (see under Algebra/Number theory 24 x 17cm. 2 volumes, 1730 pages. 1999. DM 548,- / OeS 4000,- / sFr 488,- / approx. US$ 343.00. ISBN 3-11-012771-7 Back to The Valuation Theory Home Page Last update: December 10, 1999

17. @article{AL-POPN1, Author = Alexandru, Victor And Popescu year = 1928, volume = 7, } @article{KRU3, author = krull, wolfgang , author = krull, wolfgang , title = {\ U}ber einen {E}xistenzsatz der http://math.usask.ca/fvk/Vtbibl.bib

18. Wolfgang Krull -- Facts, Info, And Encyclopedia Article wolfgang krull. Categories German mathematicians, 1971 deaths, 1899 birthswolfgang krull (1899 1971) was a (A person of German nationality) German http://www.absoluteastronomy.com/encyclopedia/w/wo/wolfgang_krull.htm

Wolfgang Krull [Categories: German mathematicians, 1971 deaths, 1899 births] Wolfgang Krull (1899 - 1971) was a (A person of German nationality) German mathematician, working in the field of (Click link for more info and facts about commutative algebra) commutative algebra See: (Click link for more info and facts about Krull dimension) Krull dimension , the (Click link for more info and facts about Krull topology) Krull topology (Click link for more info and facts about Krull's intersection theorem) Krull's intersection theorem and (Click link for more info and facts about Krull's principal ideal theorem) Krull's principal ideal theorem PrintFooter('Wolfgang_Krull') Arts Business Health Sports ... Random

19. Krull Dimension -- Facts, Info, And Encyclopedia Article named after (Click link for more info and facts about wolfgang krull) wolfgangkrull (1899 1971), is defined to be the number of strict inclusions in http://www.absoluteastronomy.com/encyclopedia/k/kr/krull_dimension.htm

Krull dimension [Categories: Commutative algebra] In (Click link for more info and facts about commutative algebra) commutative algebra , the Krull dimension of a (Jewelry consisting of a circlet of precious metal (often set with jewels) worn on the finger) ring R , named after (Click link for more info and facts about Wolfgang Krull) Wolfgang Krull (1899 - 1971), is defined to be the number of strict inclusions in a maximal chain of (Click link for more info and facts about prime ideals) prime ideals . We take the (Click link for more info and facts about supremum) supremum of chain lengths if no maximal chain can be found. For example, in the ring ( Z Z )[x,y,z] we can consider the chain Each of these ideals is prime, so the Krull dimension of ( Z Z )[x, y, z] is at least the number of strict inclusions in this chain, that is, 3. In fact the dimension of this ring is exactly 3. An alternate way of phrasing this definition is to say that the Krull dimension of R is the largest (The vertical dimension of extension; distance from the base of something to the top) height of any prime ideal of R According to this convention, a

20. Krull Dimension the krull dimension of a ring R, named after wolfgang krull (1899 1971) If a ring R has krull dimension k, then the polynomial ring Rx will have http://www.algebra.com/algebra/about/history/Krull-dimension.wikipedia

Krull dimension Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc Wikimedia needs your help in its 21-day fund drive. See our fundraising page You did it! Nearly US$220,000 has been raised . Thank you for your generosity! Krull dimension In commutative algebra , the Krull dimension of a ring R , named after Wolfgang Krull ), is defined to be the number of strict inclusions in a maximal chain of prime ideals . We take the supremum of chain lengths if no maximal chain can be found. For example, in the ring ( Z Z )[x,y,z] we can consider the chain (2) ⊂ (2,x) ⊂ (2,x,y) ⊂ (2,x,y,z) Each of these ideals is prime, so the Krull dimension of ( Z Z )[x, y, z] is at least the number of strict inclusions in this chain, that is, 3. In fact the dimension of this ring is exactly 3. An alternate way of phrasing this definition is to say that the Krull dimension of R is the largest height of any prime ideal of R According to this convention, a integral domain of dimension zero is a field Dedekind domains and discrete valuation rings have dimension one.

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