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         Homological Algebra:     more books (109)
  1. An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) by Charles A. Weibel, 1995-10-27
  2. An Introduction to Homological Algebra (Universitext) by Joseph J. Rotman, 2008-10-14
  3. A Course in Homological Algebra (Graduate Texts in Mathematics) by Peter J. Hilton, U. Stammbach, 1997-01-17
  4. An Elementary Approach to Homological Algebra (Monographs and Surveys in Pure and Applied Math) by L.R. Vermani, 2003-05-28
  5. Basic Homological Algebra (Graduate Texts in Mathematics) by M. Scott Osborne, 2000-05-19
  6. Homological Algebra (PMS-19) by Henri Cartan, Samuel Eilenberg, 1999-11-29
  7. Homological Algebra by S.I. Gelfand, Yu.I. Manin, 1999-06-22
  8. Methods of Homological Algebra (Springer Monographs in Mathematics) by Sergei I. Gelfand, Yuri I. Manin, 2010-11-02
  9. Algebras, Rings and Modules: Volume 2 (Mathematics and Its Applications) by Michiel Hazewinkel, Nadiya Gubareni, et all 2010-11-02
  10. Abelian Groups, Rings, Modules, and Homological Algebra (Lecture Notes in Pure and Applied Mathematics)
  11. Notes on Homological Algebra (Mathematics Studies) by Joseph J. Rotman, 1971-06-17
  12. Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects (Lecture Notes in Pure and Applied Mathematics)
  13. K-theory and Homological Algebra: A Seminar Held at the Razmadze Mathematical Institute in Tbilisi, Georgia, USSR 1987-88 (Lecture Notes in Mathematics)
  14. Trivial extensions of Abelian categories: Homological algebra of trivial extensions of Abelian categories with applications to ring theory (Lecture notes in mathematics ; 456) by Robert M Fossum, 1975

1. Homological Algebra - Wikipedia, The Free Encyclopedia
homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins
Homological algebra
From Wikipedia, the free encyclopedia
Jump to: navigation search Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology ) and abstract algebra (theory of modules and syzygies ) at the end of the 19th century, chiefly by Henri Poincar© and David Hilbert The development of homological algebra was closely intertwined with the emergence of category theory . By and large, homological algebra is the study of homological functors and the intricate algebraic structures that they entail. The hidden fabric of mathematics is woven of chain complexes , which manifest themselves through their homology and cohomology . Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings , modules, topological spaces , and other 'tangible' mathematical objects. A powerful tool for doing this is provided by spectral sequences From its very origins, homological algebra has played an enormous role in algebraic topology. Its sphere of influence has gradually expanded and presently includes

I wanted to teach essentially everything I knew about homological algebra and category theory, with a large dose of the kind of commutative ring theory that
A Course in Homological Algebra
E.L. Lady
In the fall of 1974, I returned to the University of Kansas after spending a year at the University of Illinois. During my time at Illinois, I had sat in on a course on Topos Theory (the most avant-garde form of category theory) given by John Gray, and had also attended the commutative ring theory seminars led by Robert Fossum, Philip Griffith, and Graham Evans. I had also spent a lot of time in the library, as usual reading on a large variety of topics, but most especially trying to understand the most recent commutative ring theory, especially as it related to algebraic geometry. Back at Kansas, the ring theorists were concerning themselves with the Gilmer-style theory of non-noetherian commutative rings, and were intimidated by any homological approach at all, even the bare mention of Ext. Paul Conrad who was the head of the algebra department (as it were) at Kansas suggested that I might like to teach a two-semester graduate topics course. I suggested that Homological Algebra might be an appropriate course. My objective was to educate the faculty as well as whatever students enrolled. And in fact, all three rings theorists Brewer, Rutter, and Philip Montgomery, attended regularly.

3. 18: Category Theory, Homological Algebra
While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in
Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields
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18: Category theory, homological algebra
Category theory, a comparatively new field of mathematics, provides a universal framework for discussing fields of algebra and geometry. While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology.
A survey article which discusses the roles of categories and topoi in twentieth-century mathematics.
Applications and related fields
The word "category" is used to mean something completely different in general topology
  • General theory of categories and functors
  • Special categories
  • Categories and algebraic theories
  • Categories with structure
  • Abelian categories
  • Categories and geometry
  • Homological algebra, see also 13DXX, 16EXX, 55UXX
This is among the smaller areas in the Math Reviews database. Browse all (old) classifications for this area at the AMS.

4. History Of Homological Algebra, By Chuck Weibel
This is a survey of the history of homological algebra, from its beginnings with Riemann and Betti, and Poincaré, to the previous decade.
History of Homological Algebra, by Chuck Weibel
This paper appeared as pp.797-836 in the book The History of Topology , ed. I.M. James, Elsevier, 1999. Chuck Weibel

5. Homological Algebra -- From Wolfram MathWorld
An abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra.
Applied Mathematics

Calculus and Analysis

Discrete Mathematics
... Miscellaneous Algebras
Homological Algebra An abstract algebra concerned with results valid for many different kinds of spaces Modules are the basic tools used in homological algebra. SEE ALSO: Commutative Diagram Diagram Chasing Diagram Lemma Module REFERENCES: Enochs, E. E. and Jenda, O. M. G. Relative Homological Algebra. Berlin: de Gruyter, 2000. Hilton, P. and Stammbach, U. A Course in Homological Algebra, 2nd ed. New York: Springer-Verlag, 1997. Weibel, C. A. An Introduction to Homological Algebra. New York: Cambridge University Press, 1994.
Weisstein, Eric W.
"Homological Algebra." From MathWorld A Wolfram Web Resource. Contact the MathWorld Team
Wolfram Research, Inc.
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6. Cartan, H. And Eilenberg, S.: Homological Algebra (PMS-19).
of the book homological algebra (PMS19) by Cartan, H. and Eilenberg, S., published by Princeton University Press.......
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When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

7. Thoughts On Homological Algebra « Fightin’ The Resistance Of Matter
So I’ve passed my homological algebra exam. Today morning, I unexpectedly realized that I’m going to have a mathematics exam (yes… with the great pain I
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Thoughts on Homological Algebra
March 10, 2007 ) almost always discouraged me. Correspondingly, my knowledge of derived/triangulated categories, simplicial objects and derived functors of nonadditive functors (these were the main topics of a course) is a little bit like a knowledge of history - I know essential facts, I even see some causal connections between them, but I miss something - a spirit of mathematics?. love to know how (for example) Terrence Tao learned HA (as everybody probably knows, there is non-zero chance of meeting him around, so who knows :-). My General Theory of Geniuses (;-) predicts that he (or maybe He?:-) spent as much time as I did (or less, of course) on the given topic, but his unconsciousness checked all the details and communicated them to his consciousness, one day or another (actually, my GTG says that my unconsiousness also checked all the details, but it saved them for itself, damn bastard.) I believe you may find it worth reading if you already know some basics of HA (nothing more than classical derived functors Comments are appreciated.

8. LMS-EPSRC Short Course: Homological Algebra And Equivariant Homology
homological algebra is at the heart of algebra, topology and geometry. The aim of the short course is to provide an introduction to this wide and classical
LMS/EPSRC Short Course: Homological Algebra and Equivariant Homology
9 July to 13 July 2007
School of Mathematics
University of Southampton
Peter Kropholler (Glasgow)
Brita Nucinkis (Southampton)
also Ian Leary (Ohio State)
Organisers: Peter Kropholler and Brita Nucinkis
Homological algebra is at the heart of algebra, topology and geometry. The aim of the short course is to provide an introduction to this wide and classical field. More precisely, the goal is to provide a general understanding of the basic concepts involved and give an introduction to some applications in the cohomology of groups, algebraic topology and equivariant homology theories.
The lecture series will start on Monday morning and finish on Friday. On Monday, registration will begin at 9:00; the first lecture will start at 9:30. On Friday afternoon there will be a special lecture. All lectures and tutorials will take place in Lecture Theatre 4A, Building 54 (School of Mathematics) on Highfield Campus.

9. Mathematical Sciences Research Institute - Commutative Algebra: Interactions Wit
Commutative Algebra Interactions with homological algebra and Representation Theory Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA
Choose a Destination... Calendar Programs Workshops Summer Grad Workshops Seminars Events/Announcements Application Materials Visa Information Propose a Program Propose a Workshop Policy on Diversity MSRI Alumni Archimedes Society Why Give to MSRI Ways to Give to MSRI Donate to MSRI Planned Gifts FAQ Staff Member Directory Contact Us Directions For Visitors Pictures Library Computing SGP Streaming Video / VMath MSRI in the Media Emissary Newsletter Outlook Newsletter Subscribe to Newsletters Books, Preprints, etc. Federal Support Corporate Affiliates Sponsoring Publishers Foundation Support Academic Sponsors
Commutative Algebra: Interactions with Homological Algebra and Representation Theory
February 03, 2003 to February 07, 2003 Organized By: Luchezar Avramov (chair), Ragnar Buchweitz, and John Greenlees Parent Programs: Commutative Algebra Participant List: View a List of Registered Participants Recently, commutative algebra has been developing new connections with a variety of fields, and adding new directions to some traditional links. This interdisciplinary workshop proposes to generate an active exchange of information between practitioners and consumers of commutative algebra. The subjects discussed will include invariant theory, cohomology of groups, free resolutions, rational homotopy, stable homotopy, representation theory, and derived categories.
The following have accepted invitations to speak:
W. Bruns

10. Homological Algebra
Diagram from homological algebra (TraditionalForm). HeisenbergEuler Lagrangian Zeta Function Sums Any questions about topics on this page?
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11. MATHnetBASE: Mathematics Online
homological algebra was developed as an area of study almost 50 years ago, and many books An Elementary Approach to homological algebra fills that void.

12. Non-abelian Homological Algebra
This Bibliography lists some papers and books on multiple categories and groupoids, nonlinear homological algebra, and related areas directly relevant to
Last updated 7 July, 2004
Some publications in non-abelian homological algebra
This Bibliography lists some papers and books on multiple categories and groupoids, non-linear homological algebra, and related areas directly relevant to the themes developed in the accompanying article on Higher dimensional group theory The list is not complete, and should be thought of more as an entry point into the literature. It is hoped to develop it over time. The paper "Some problems in non abelian homological and homotopical algebra" gives some 35 problems or problem areas in this field. I have given a separate and fuller bibliography on the non abelian tensor product. This bibliography should be related to papers on Lie groupoids, Lie algebroids and Lie pseudoalgebras in a bibliography compiled by Kirill Mackenzie. Papers added in 2004 are coloured brown.
  • R.Aboughazi, `Produit tensoriel du groupe d'Heisenberg', Bull. Soc. Math. France, 15, 95-106, 1987.
  • G. Abramson, J.-P.Meyer, J.Smith, `A higher dimensional analogue of the fundamental groupoid', in Recent developments of algebraic topology, RIMS Kokyuroku 781, Kyoto, 38-45, 1992.
  • F.Al-Agl, Aspects of multiple categories, University of Wales PhD Thesis, 1989.
  • 13. Basic Homological Algebra - K-Theory Journals, Books & Online Media | Springer
    Basic homological algebra Algebra. This book is intended for one-quarter or one semester-courses in homological algebra. The aim is to cover Ext and Tor

    14. Homological Algebra
    Certain results in homological algebra regarding spectral sequences have been repeatedly used in various contexts. The usual reference has been to
    Next: Motives Up: Current Mathematical Research Previous: Rationality and Unirationality
    Homological Algebra
    Certain results in homological algebra regarding spectral sequences have been repeatedly used in various contexts. The usual reference has been to unpublished work of Deligne for a proof. The general applicability of these results has been a matter of some interest due to the interest in ``motives'' (see below). The author has generalised and clarified the existence and properties of the constructions used; roughly speaking this is a theory of spectral sequences of spectral sequences. Recent discussions with B. Kahn (CNRS) have led to a further generalisation of the results to unbounded complexes. A paper based on this work has appeared in the Journal of Algebra. A talk based on this work was also presented at the ICM Satellite conference at Essen.
    Kapil H. Paranjape 2000-04-26

    15. Homological Algebra Of Twisted Quiver Bundles -- Gothen And King 71 (1): 85 -- J
    homological algebra of Twisted Quiver Bundles. Peter B. Gothen and Alastair D. King. Departamento de Matemática Pura, Faculdade de Ciências, Universidade do
    @import "/resource/css/hw.css"; @import "/resource/css/jlms.css"; Skip Navigation Oxford Journals Previous Article Next Article Journal of the London Mathematical Society 2005 71(1):85-99; doi:10.1112/S0024610704005952
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    Homological Algebra of Twisted Quiver Bundles
    Peter B. Gothen and Alastair D. King
    Mathematical Sciences, University of Bath Claverton Down, Bath BA2 7AY, United Kingdom, Received 18 July 2003. Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed space. It

    16. [math-ph/0112031] Homological Algebra Of Multivalued Action Functionals
    homological algebra of multivalued action functionals. Authors E. Aldrovandi (Florida State University) Comments 9 pages, AMSLaTeX (amsart class). math-ph
    Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
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    Mathematical Physics
    Title: Homological algebra of multivalued action functionals
    Authors: E. Aldrovandi (Florida State University) (Submitted on 15 Dec 2001 ( ), last revised 26 Mar 2002 (this version, v2)) Abstract: We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally defined variational equations. Comments: 9 pages, AMSLaTeX (amsart class). Version to appear in Letters in Mathematical Physics Subjects: Mathematical Physics (math-ph) ; High Energy Physics - Theory (hep-th); Algebraic Topology (math.AT); Differential Geometry (math.DG) Journal reference: Lett.Math.Phys. 60 (2002) 47-58 Report number: Cite as: arXiv:math-ph/0112031v2
    Submission history
    From: Ettore Aldrovandi [ view email
    Sat, 15 Dec 2001 06:39:28 GMT (15kb)

    17. Introduction To Homological Algebra, 85 - Elsevier
    Introduction to homological algebra, 85 To order this title, and for more information, click here By Joseph Rotman, University of Illinois, Urbana
    Home Site map Elsevier websites Alerts ... Introduction to Homological Algebra, 85 Book information Product description Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view INTRODUCTION TO HOMOLOGICAL ALGEBRA, 85
    To order this title, and for more information, click here
    Joseph Rotman
    , University of Illinois, Urbana
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    Hardbound, 400 pages, publication date: JUN-1979
    ISBN-13: 978-0-12-599250-3
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    Price: Order form USD 108 EUR 106 GBP 71 Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries. See also information about , and links to our regional sales offices Last update: 8 Feb 2008 Reviews Submit your review Bookmark this page Recommend this publication Overview of all books ... Feedback A Reed Elsevier company Elsevier B.V.

    18. Homological Algebra Modulo A Regular Sequence With Special
    Let M be a finite module over a ring R obtained from a commutative ring Q by factoring out an ideal generated by a regular sequence. The homological

    19. Free Books > Nonfiction > Philosophy > Logic & Language > Categories, Derived Ca
    Categories, Derived Categories, homological algebra. by Pierre Schapira Seminar in Algebra and Number Theory Rational Points on Elliptic Curves,
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    20. Internet Archive: Details: Homological Algebra
    homological algebra ( 00, 1956). homological algebra ( 00, 1956). Author Cartan,Henri. Title, homological algebra. Creator, Cartan,Henri.
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    Homological Algebra Author: Cartan,Henri. Book Contributor: Osmania University Language: English Keywords: NATURAL SCIENCES Mathematics Algebra
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