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Topic: Homological algebra

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	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 areas of ring theory, group theory, and algebraic topology.
		Homological algebra, by Henri Cartan and Samuel Eilenberg.
		An introduction to homological algebra / Joseph J. Rotman.
	www.math.niu.edu /~rusin/known-math/index/18-XX.html (286 words)

	People Algebra Math Science
		Algebraic number theory; algebraic geometry; group theory (finite, finitely generated, compact, or algebraic); homological algebra; algebraic combinatorics; applied algebra.
		Algebraic Topology; K-theory; Homological Algebra and Deformation Theory.
		Representation theory of finite dimensional algebras; Vector bundles on curves and surfaces; Invariant theory and the study of rings with polynomial identities.
	www.iaswww.com /ODP/Science/Math/Algebra/People (587 words)

	Amazon.com: Books: A Course in Homological Algebra (Graduate Texts in Mathematics) (Site not responding. Last check: 2007-11-06)
		An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) by Charles A. Weibel
		A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics) by J.
		Algebraic topology is given a rigorous foundation in this book and readers with a background in that subject will appreciate the discussion more.
	www.amazon.com /exec/obidos/tg/detail/-/0387948236?v=glance (766 words)

	Algebra
		The document Graduate Study in Algebra outlines the general areas of algebra studied here and describes the advanced undergraduate and graduate courses that are offered regularly.
		Commutative algebra, polynomials in several variables, homological algebra, ring theory.
		Algebraic graph theory, graph theory, combinatorial group theory, combinatorics.
	www.math.uiuc.edu /GraduateProgram/researchmath/algebra.html (251 words)

	13: Commutative rings and algebras
		Of particular interest are several classes of rings of interest in number theory, field theory, algebraic geometry, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra.
		Typically one classifies problems as Algebraic Geometry when stated in terms of points, hypersurfaces, divisors, and other geometric objects, and as Commutative Algebra when stated in terms of ideals and coordinate rings, although in practice techniques from both areas are used in tandem.
		The algebraic study of general collections of polynomials is appropriate for this field; the study of individual polynomials or specific collections usually belongs elsewhere.
	www.math.niu.edu /~rusin/known-math/index/13-XX.html (2760 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Homological Algebra Homological methods arose in the 19th century in the work of Riemann and Poincare, who were studying the shape of various kinds of space.
		The algebraic methods for doing this by 1945 had become a subject in their own right --- Homological Algebra.
		Homological methods have important applications in many other fields besides Algebraic Topology, such as Algebraic Geometry, Commutative Rings, Group Theory, Invariant Theory, Number Theory, and Combinatorics.
	www.mast.queensu.ca /~robertsl/math411/homalg.txt (240 words)

	Algebra and Algebraic Topology Home Page
		The research in algebra at Bangor has to a large extent been motivated by problems in algebraic topology and homological algebra.
		The connections between algebraic topology, homological algebra and areas of "pure" algebra, number theory and algebraic geometry have remained very strong.
		The theory of crossed modules of groups started with their occurrence in algebraic topology, but they also occur naturally in the study of automorphisms of groups and in combinatorial group theory with the free crossed module generated by a presentation of a group.
	www.informatics.bangor.ac.uk /public/mathematics/research/algtop/algtop2.html (1545 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		This example shows that traditional homological algebra is encompassed by Quillen's homotopical algebra, and indeed this unification was one of the main points of Quillen's influential work [Qui67 ].
		Pure homological algebra has applications to phantom maps in the stable homo- topy category [CS98 ] and in the (usual) derived category of a ring [Chr98 ], connections to Kasparov KK-theory [Sch01 ], and is actively studied by algebraists and representation theorists.
		In addition to the connection between phantom maps and pure homological algebra, the authors are interested in the pure derived category as a tool for connecting the global pure dimension of a ring R to the behaviour of phantom maps in DC and DP under composition.
	jdc.math.uwo.ca /papers/relative.txt (10317 words)

	Amazon.ca: Books: Methods of Homological Algebra (Site not responding. Last check: 2007-11-06)
		This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors.
		The book addresses people who want to learn a modern approach to homological algebra and to use it in their work.
		Addresses people who want to learn a modern approach to homological algebra and to use it in their work.
	www.amazon.ca /exec/obidos/ASIN/3540435832 (294 words)

	Siamak Yassemi
		Teaching Assistant (courses for commutative algebra and homological algebra, Institute for Mathematical Sciences, University of Copenhagen, Denmark.
		Doctoral studies in commutative and homological algebra, Institute for Mathematical Sciences, University of Copenhagen, Denmark.
		A.R. Naghipour, Reductions in commutative algebra, 1998, University of Tehran.
	math.ipm.ac.ir /yassemi/vita.htm (590 words)

	Cornell Math - Math 740 (SP01)
		Homological Algebra is a common language for many mathematical disciplines where the global properties of objects are essential.
		The purpose of this course is to provide an introduction to the subject, basically from algebraic and algebro-geometric perspective.
		We shall try to adopt the modern approach to Homological Algebra based on a systematic use of the notion of derived and triangulated categories.
	www.math.cornell.edu /~www/Courses/GradCourses/SP01/740.html (82 words)

	Amazon.com: Books: An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) (Site not responding. Last check: 2007-11-06)
		Simon (Series Editor) "Homological algebra is a tool used in several branches of mathematics: algebraic topology, group theory, commutative ring theory, and algebraic geometry come to mind..." (more)
		Homological algebra is a tool used in several branches of mathematics: algebraic topology, group theory, commutative ring theory, and algebraic geometry come to mind.
		Now Homological Algebra is not a simple subject that can be picked up with only a minimal background.
	www.amazon.com /exec/obidos/tg/detail/-/0521559871?v=glance (913 words)

	Commutative Algebra: Homological and Birational Theory
		These invariants are an analogue of traditional multiplicities in Algebraic Geometry and record the action of the Frobenius homomorphism on a ring in positive characteristic.
		Rees algebras are the rings in which integral dependence of ideals can be studied and they are the algebraic objects that appear in the process of resolution of singularities.
		Rees algebras have been used in Kawasaki's celebrated proof of the existence of Macaulifications, a weak form of resolution of singularities.
	www.pims.math.ca /birs/workshops/2004/04w5027 (1320 words)

	An Introduction to Homological Algebra - Cambridge University Press
		The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician.
		The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences.
		The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521559871 (251 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Abstract: An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is encompassed by Quillen's homotopical algebra.
		The goal of this paper is to show how more general forms of homological algebra also fit into Quillen's framework.
		The motivation for the work is the construction of the "pure derived category" of a ring R. Pure homological algebra has applications to phantom maps in the stable homotopy category and the (usual) derived category of a ring, and these connections will be described.
	hopf.math.purdue.edu /Christensen/derived.abstract (194 words)

	MATHnetBASE: Mathematics Online
		Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist.
		Often perceived as dry and abstract, homological algebra nonetheless has important applications in many important areas.
		Beyond making classical homological algebra accessible to students, the author's level of detail, while not exhaustive, also makes the book useful for self-study and as a reference for researchers.
	www.mathnetbase.com /ejournals/books/book_summary/summary.asp?id=1198 (206 words)

	NDSU Club Math Page (Site not responding. Last check: 2007-11-06)
		This talk will give an overview about what homological algebra is and some of the ideas and applications that motivate it.
		Homological algebra is a discipline of mathematics in its own right, but in this talk we will concentrate on homological algebra as a tool for other branches of math.
		The aim of this talk is to be much more on the intuitive side (that is, we will sacrifice rigor for intuitive understanding where appropriate) and I encourage everyone to be there.
	www.math.ndsu.nodak.edu /mathclub/coykendall5.html (95 words)

	Untitled Document (Site not responding. Last check: 2007-11-06)
		In this course we will study the basic notions of homological algebra concentrating on the cohomology of finite and profinite groups.
		To be a little more precise on what we will likely cover, as preliminary material, we will (somewhat quickly) go over some of chapter 1 and most of chapters 2 and 3.
		Anything we do about division algebra, quadratic forms, and K-theory is not contained in the text; other references will be given.
	www.math.nmsu.edu /graduate_information/pat.html (158 words)

	Cartan, H. and Eilenberg, S.: Homological Algebra (PMS-19).
		When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra.
		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.
	pup.princeton.edu /titles/250.html (240 words)

	Homological Algebra (Site not responding. Last check: 2007-11-06)
		Certain results in homological algebra regarding spectral sequences have been repeatedly used in various contexts.
		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.
	www.imsc.ernet.in /~kapil/work/node14.html (118 words)

	Homological Algebra
		Often Homological Algebra is considered as a tool that provides a unified language to problems in various fields in Algebra and in Algebraic Topology and that offers various kinds of constructions which are helpful in proofs (e.g.
		The focus of this course is on applications: We introduce homological methods (of course), and see how they work in the context of linear algebra problems, like the study of systems of linear maps, or of subspace problems.
		Weibel, An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press 1994.
	www.math.fau.edu /Schmidme/homology.html (366 words)

	Relative Homological Algebra (Site not responding. Last check: 2007-11-06)
		Since the introduction of relative homological algebra in 1965, more theorems have been found to guarantee the existence of precovers, covers, preenvelopes and envelopes.
		These are the basic objects of the subject and are used to construct resolutions and then left and right derived functions.
		Other chapters discuss: torsion free covering modules; covers; envelopes; covers, envelopes and cotorsion theories; relative homological algebras and balance; Iwanaga-Gorenstein and Coker-Macauley rings and their modules; Gorenstein modules; Gorenstein covers and envelopes; and balance over Gorenstein and Cohen-Macauley rings.
	www.booknews.co.uk /Books/1348.htm (166 words)

	Algorithms In Algebraic Topology And Homological Algebra: Problem Of Complexity (ResearchIndex)
		5 Cyclic homology of commutative algebras (context) - Burghelea, Vigue - 1986
		1 E#ective algebraic topology (context) - Schon - 1991
		1 Homological perturbation theory, Hochschild homology, and fo..
	citeseer.ist.psu.edu /549115.html (643 words)

	Cornell Math - MATH 740, Spring 1999
		The subject of homological algebra grew out of algebraic topology but has developed a life of its own, and now its influence can be felt in many areas of modern mathematics.
		There is a rather nice recent book by Charles Weibel called "An Introduction to Homological Algebra" which will serve as a sort of textbook for the course.
		Prior knowledge of algebraic topology is not assumed, but connections with topology will be sketched when appropriate.
	www.math.cornell.edu /~www/Courses/GradCourses/SP99/740.html (174 words)

	Publisher description for Library of Congress control number 00058588 (Site not responding. Last check: 2007-11-06)
		It presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of delta-good approximations for quasi-hereditary algebras and reductive groups.
		The book provides a detailed introduction to homological algebra, commutative ring theory and homological theory of comodules of co-algebras over an arbitrary base.
		This book will be of interest to researchers and graduate students in algebra, specialising in commutative ring theory and representation theory.
	www.loc.gov /catdir/description/cam021/00058588.html (156 words)

	Some Selected Publications (Site not responding. Last check: 2007-11-06)
		Perturbation Theory in Differential Homological Algebra I, with V.K.A.M. Gugenheim, IL.
		Perturbation Theory in Differential Homological Algebra II, with V.K.A.M. Gugenheim and Jim Stasheff, IL.
		Algebraic Aspects of the Quantum Yang-Baxter Equation, with David Radford, Journal of Algebra, 154 (1993), 228-288.
	www.matematik.su.se /~lambe/public/pubs.html (805 words)

	History Of Homological Algebra (ResearchIndex)
		32 Homological Algebra (context) - Cartan, Eilenberg - 1956
		8 Commutative algebras and cohomology (context) - Harrison - 1962
		1 Algebraic vector bundles on -- n and problems of linear alge..
	citeseer.ist.psu.edu /260176.html (1009 words)

	UWM Math: Algebra Group (Site not responding. Last check: 2007-11-06)
		The department offers a bridge course in algebra (631-632) covering undergraduate material at a more advanced level and pace and a "true" graduate algebra course (731-732) every year.
		Recent topics have included Hopf algebras and quantum groups, homological algebra, non-commutative algebraic geometry á la Artin, van der Bergh, et al., Gröbner bases, symmetric functions and representations of the symmetric group, Kac-Moody Lie algebras.
		Non-commutative Algebraic Geometry: this is a fledgling field for us, so we've linked you to a web page by Paul Smith at the University of Washington
	www.uwm.edu /Dept/Math/Research/Algebra/algebra.html (275 words)

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