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Topic: List of commutative algebra topics

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	Commutative algebra - Definition, explanation
		In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras.
		Given the scheme concept, commutative algebra is reasonably thought of as either the local theory or the affine theory of algebraic geometry.
		The general study of rings that are not required to be commutative is known as noncommutative algebra; it is pursued in ring theory, representation theory and in other areas such as Banach algebra theory.
	www.calsky.com /lexikon/en/txt/c/co/commutative_algebra.php (573 words)

	Graduate Study in Algebra
		Algebra is one of the oldest branches of mathematics, and the study of algebra in the Department of Mathematics has traditionally been rich and strong.
		The research strengths of the faculty are in the theory of rings (commutative and noncommutative), the theory of groups, algebraic number theory, the representation theory of groups and algebras, and algebraic geometry.
		The core graduate courses in algebra are Abstract Algebra I and II (Math 500 and 501).
	www.math.uiuc.edu /GraduateProgram/researchmath/gradalgebra.html (1660 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.
		Other topics of arithmetic and combinatorial interest include the study of finite commutative rings (including such classic results as Wedderburn's theorem: finite integral domains are fields), and the study of Witt rings (related to power-series rings and particularly useful for studying rings in finite characteristic).
		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.
	www.math.niu.edu /~rusin/known-math/index/13-XX.html (2760 words)

	CRC Press Online
		In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics.
		Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups.
		This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy.
	www.crcpress.com /shopping_cart/products/product_detail.asp?sku=C5521&parent_id=781&pc= (470 words)

	PlanetMath: algebra
		This is version 9 of algebra, born on 2001-10-19, modified 2005-04-10.
		Object id is 353, canonical name is Algebra.
		While this entry may be technically correct, I still woulden't know what algebra was by reading it ;) May I suggest a short history of the invention of algebra, as well something to to tune of "a system to manipulate mathematical formulas"
	planetmath.org /encyclopedia/Algebra.html (199 words)

	Algebra -- Resources (Site not responding. Last check: )
		Algebraic Areas of Mathematics - Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra.
		Robbins Algebras Are Boolean - A web text by William McCune describing the solution of this problem by a theorem-proving program, with input files and the proofs.
		Universal Algebra is a technical branch of mathematics related to algebra and model theory.
	www.edinformatics.com /algebra.htm (669 words)

	Introduction to Commutative Algebra: Current Amazon U.S.A. One-Edition Data
		Some people believe that, for getting into algebraic geometry (by this I mean Grothendieck-like AG, with schemes and all that), one needs a monolithic training in commutative algebra (something like both volumes of Zariski-Samuel, for example).
		Masterful choice of topics, great exercises (as a matter of fact, about half the topics of the book, and more specifically the ones that are directly related to AG, are treated in the exercises, some of them quite challenging) - like one said before, it looks like a "chapter 0" of Hartshorne's book on AG.
		The authors consciously estabilish relations between the commutative algebra and the modern foundations of AG over and over along the way, illuminating both topics.
	www.negative-procreative.biz /stuff-0201407515.html (899 words)

	Computer Algebra, Theorem Proving, and Types (Site not responding. Last check: )
		Many computations a mathematician performs can be described in "algebraic" terms, that is, as dealing with various symbolic entities that are combined in restricted ways and are subject to laws (e.g., equations) specifying which combinations are equivalent.
		The term "computer algebra", as it appears in my title, has this general sense (as opposed to the more restrictive sense of "computational commutative algebra"), and my talk will discuss this subject and its relation to automatic theorem proving and type theory.
		A survey of examples of computer algebra drawn from several areas of mathematics, including commutative algebra and algebraic geometry, invariant theory, (algebraic) number theory, group theory, Lie algebra, combinatorics, algebraic topology, and analysis (scientific computation).
	www.cs.cornell.edu /Nuprl/PRLSeminar/PRLSeminar94_95/Wilson/Oct4.html (200 words)

	Math 252: Commutative Algebra and Algebraic Geometry
		Commutative algebra forms the foundation on which Algebraic Geometry and Algebraic Number Theory are built.
		Prime, maximal, and radical ideals, algebras and the category of finitely generated, reduced algebras over an algebraically closed field, statements of the basis theorem and the Nullstellensatz, contraction and extension of ideals, Chinese Remainder Theorem, review of Groebner bases and applications.
		The following topics are strictly algebraic geometry topics and are treated in the algebraic geometry course which has Math 252 as a prerequisite: Coherent sheaves, quasi-projective varieties and their morphisms, rational maps, Weil and Cartier divisors, intersection theory.
	www.math.duke.edu /graduate/courses/spring02/math252.html (347 words)

	commalg.org - the center for commutative algebra
		The retirement is motivated by the success of the Commutative Algebra (AC) section of the arXiv preprint server.
		If you are an active commutative algebraist who is not on the list, or if you would like your information changed, click here to let us know.
		For example, links to certain mathematical journals and some Computer Algebra Systems can be found there.
	www.commalg.org (439 words)

	Gourt :: Science :: Math :: Algebra
		Algebraic Areas of Mathematics: Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra.
		Center for Commutative Algebra: A site for the commutative algebra community, including news, conference and preprint announcements, and a huge list of algebraists.
		Robbins Algebras Are Boolean: A web text by William McCune describing the solution of this problem by a theorem-proving program, with input files and the proofs.
	science.gourt.com /Math/Algebra.html (573 words)

	Amazon.ca: Books: The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry (Site not responding. Last check: )
		Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems.
		It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already.
		As an aid to the reader, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics.
	www.amazon.ca /exec/obidos/ASIN/0387222154 (429 words)

	The Math Forum - Math Library - Linear Algebra (Site not responding. Last check: )
		Algebraic Algorithms - Susan Landau; Univ. of Massachusetts at Amherst
		Category theory is a recent branch of mathematics originating in algebraic topology, but rapidly establishing connections with algebra, logic, algebraic and differential geometry, and most recently computer science.
		A college algebra course to provide students with an understanding of the general concepts of relation and function and specifically of polynomial, exponential, and logarithmic functions; with the ability to solve system of equations by utilizing matrices...more>>
	mathforum.org /library/topics/linear (2236 words)

	foodroom.com -- - Science - Math - Algebra - People
		Commutative algebra, finite abelian groups, combinatorics and number theory: especially factorization of elements in integral domains and monoids.
		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.foodroom.com /directory/Science/Math/Algebra/People (402 words)

	[No title] (Site not responding. Last check: )
		The low level of activity for this list is not a negative indicator of its value.
		In order to get a broader view of list activity, I searched the 1991 calendar year archives within which 50 messages were posted.
		One message notified subscribers of a downloadable software package, version 1.35 of the "Pari package for number theory." Sample topics during the review period were: Carmichael numbers, the rational parameterization of Diophantine equations, and a request for citation on a simple proof of the infinitude of primes (Euler got the credit).
	www.umsl.edu /~muns/proddir/rev1n05.htm (435 words)

	Directory - Science: Math: Algebra: People
		Varieties of groups; finite permutation groups; infinite permutation groups; design of group-theoretic algorithms; soluble groups; quantitative topics in group theory; matrices over finite fields; miscellaneous questions in combinatorics, geometry and general group theory; history of group theory.
		Colleagues in General Algebra and Related Fields · cached · A list compiled by Emil W. Kiss, Ágnes Szendrei and Keith Kearnes.
		Commutative Algebraists · iweb · cached · List of email and web addresses at the Center for Commutative Algebra.
	www.incywincy.com /default?p=933004 (344 words)

	Books on Algebra (Site not responding. Last check: )
		It probably represents the strongest influence on the graduate algebra course I teach.
		This covers many of the important topics in both commutative and non-commutative ring theory in quite a bit of detail.
		The original edition of this book is very nice, because it has good information on a wide variety of topics, such as Dedekind domains, modules over artinian rings, and the like.
	www.math.hawaii.edu /~lee/algebra/references.html (553 words)

	GoForIt.com's Directory - Science: Math: Algebra
		Algebra is a branch of mathematics that uses letters or other symbols to represent unknown quantities, called variables.
		Another part of this topic is graphing of equations and functions using the Cartesian coordinate graph or polar coordinates.
		Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra.
	search.goforit.com /default?p=26916 (550 words)

	The Graduate School at NDSU
		By the end of their second semester, students select an advisory committee and develop a plan of study specifying how all degree requirements are to be met..
		Topics include three-dimensional manifolds, knots, embedded graphs, chirality, topological rubber gloves, Möbius ladders, topology of DNA, tangles, and the Ernst-Sumners theorem.
		The ideal theory of commutative rings, structure of (non-commutative) rings, and selected advanced topics.
	www.ndsu.nodak.edu /gradschool/bulletin/d_maths.html (2432 words)

	Categories Home Page
		A list including email aliases for subscribers to this list, among many others, is the structures directory maintained by Vaughan Pratt.
		This year the conference topics are algebraic topology, category theory, and differential geometry.
		The aim of the workshop is to provide a forum for researchers to present their results to those members of the computer science and logic communities who study or apply the fixed point operation in the different fields and formalisms.
	www.mta.ca /~cat-dist/categories.html (3650 words)

	Introduction to Commutative Algebra (Site not responding. Last check: )
		This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject.
		Commutative Algebra : with a View Toward Algebraic Geometry (Graduate Texts in Mathematics)
		Commutative Ring Theory (Cambridge Studies in Advanced Mathematics)
	494062.onlinesportdiscount.com /3439343036322d312d30323031343037353135.html (894 words)

	Advanced Modern Algebra by Joseph J. Rotman [ISBN: 0130878685] - Find Cheap Textbook Prices & Save BIG
		Chapter topics include groups; commutative rings; modules; principal ideal domains; algebras; cohomology and representations; and homological algebra.
		For example, my undergraduate Algebra text was Hungerford's and post completion the logical step, being familiar with his style, was to purchase Hungerford's graduate text.
		But this failure is minimal since, at present, the majority of Algebra texts, fail to adequately introduce and motivate Finite Fields.
	www.gettextbooks.com /isbn_0130878685.html (1316 words)

	Basic Library List-Algebra
		The Theory of Equations with an Introduction to the Theory of Binary Algebraic Forms, Mineola, NY: Dover, 1960.
		Algebra I: Basic Notions of Algebra New York, NY: Springer-Verlag, 1990.
		Elements of Mathematics: Commutative Algebra, New York, NY: Springer-Verlag, 1989.
	www.maa.org /BLL/algebra.htm (1565 words)

	Powell's Books - Introduction to Commutative Algebra & Algebraic Geometry by Ernst Kunz
		The center of gravity lies in commutative algebra, and this book can serve as a preparation for more advanced topics.
		The subject of the book is not restricted to commutative algebra developed as a pure discipline for its own sake, nor is it aimed only at algebraic geometry where the intrinsic geometry of a general n-dimensional variety plays the central role.
		The dimension of affine algebras and affine algebraic varieties 4.
	www.powells.com /cgi-bin/biblio?isbn=0817630651 (603 words)

	Snowbird conference
		Injective modules are covered in most courses on commutative algebra, but we realize that you may not have had such course.
		The topic of the summer school will be commutative algebra, with special emphasis on topics that are related to local cohomology and its interactions with other areas of mathematics such as algebraic geometry, topology, and D-modules.
		Scientific background relevant to the conference topics; please indicate your student status, whether you have an advisor, and why you are interested in the conference.
	www.math.purdue.edu /~walther/snowbird.html (673 words)

	ScienceDaily -- Browse Topics: Science/Math/Algebra/People (Site not responding. Last check: )
		Commutative Algebraists - List of email and web addresses at the Center for Commutative Algebra.
		Colleagues in General Algebra and Related Fields - A list compiled by Emil W. Kiss, Ãgnes Szendrei and Keith Kearnes.
		The general inverse problem of Galois theory both for algebraic number fields and for arbitrary fields.
	www.sciencedaily.com /directory/Science/Math/Algebra/People (839 words)

	Math on the Web: Mathematics by Topics
		Mathematics by Topic lists some topic keywords in the Table of Contents.
		List of locations of the Archives of the newsgroup
		This list is maintained by Robert Fourer (4er@iems.nwu.edu) and the Optimization Technology Center of Northwestern University and Argonne National Laboratory.
	www.ams.org /mathweb/mi-mathbytopic.html (1807 words)

	Powell's Books - Algebra by Thomas W. Hungerford
		The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry
		"Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents.
		Each topic is followed by many illustrative examples and almost every section is followed by a long list of exercises of varying degrees of difficulty."
	www.powells.com /cgi-bin/biblio?inkey=17-0387905189-0 (491 words)

	Amazon.co.uk: Algebra (Graduate Texts in Mathematics): Books (Site not responding. Last check: )
		For that class we used Gallian's text "Contemporary abstract algebra." I was not fully satisfied with the text's applied flavor so I used Artin's and Herstein's texts as supplements.
		Lang's text is probably better suited for a second class in algebra at the graduate level (there are some other advanced tests such as Jacobson's, but I believe that Lang's text is the only well written text book in algebra which covers such a wide range of topics in proper detail).
		In fall 1999, my freshman year, I will take graduate algebra and graduate real analysis, I hope after those classes I will be able to tackle Lang's text in a more reasonable manner.
	www.amazon.co.uk /exec/obidos/ASIN/038795385X (820 words)

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