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Topic: Commutative algebra

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	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.
		In the case of geometric algebras, this is the setting for families of subvarieties, including nested and intersecting ones.
		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)

	Mathematical Sciences Research Institute - Commutative Algebra (Site not responding. Last check: 2007-11-02)
		Commutative algebra comes from several sources: the 19th century theory of equations, number theory, invariant theory and algebraic geometry.
		A famous example of such encoding is the translation of an abstract finite simiplicial complex into an ideal represented by the zeroes of square-free monomials in a set of variables corresponding to the vertices of the simplicial complex.
		Of course, the existing body of work in commutative algebra is not tailored to suit all new demands.
	www.msri.org /calendar/programs/ProgramInfo/17/show_program (526 words)

	Home Page of Robert B. Ash (Site not responding. Last check: 2007-11-02)
		The prerequisite is a standard graduate course in algebra.
		Commutative algebra is the theoretical foundation of algebraic geometry and algebraic number theory.
		Assuming as prerequisite a standard graduate algebra course, we attempt to reach an advanced level quickly and efficiently.
	www.math.uiuc.edu /~r-ash (123 words)

	Amazon.com: Commutative Algebra : with a View Toward Algebraic Geometry (Graduate Texts in Mathematics): Books: David ... (Site not responding. Last check: 2007-11-02)
		Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.
		The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics.
		It has seemed to me for a long time that commutative algebra is best practiced with knowledge of the geometric ideas that played a great role in its formation: in short, with a view toward algebraic geometry.
	www.amazon.com /exec/obidos/tg/detail/-/0387942696?v=glance (1702 words)

	[No title]
		Algebraic Hilton-Milnor Theorem One of the first results established utilizing this looking-glass approach wa* *s an alge- braic version of the classic Hilton-Milnor theorem.
		Of course, results about commutative algebras and their homology need not exc* *lu- sively come as parallels of topological results.
		In fact, novel results about * simplicial commutative* algebras and their homotopy and homology may point to new results in topology.
	www.math.purdue.edu /research/atopology/Turner/looking-glass.txt (3199 words)

	MC440 Commutative Algebra (Site not responding. Last check: 2007-11-02)
		Commutative algebra is a beautiful subject in its own right but is also important for the study of algebraic geometry (and the study of polynomial rings in several variables) and algebraic number theory (and the study of the integers).
		This module aims to develop an understanding of commutative algebra and to indicate its applications to other areas of mathematics.
		To determine the properties of a ring or module and be able to investigate the ideal structure of a commutative ring.
	www.mcs.le.ac.uk /Modules/Year3_98-99/MC440.html (791 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		Commutative algebra emerged during the 19th century at the crossroads of number theory, invariant theory, and algebraic geometry.
		Other significant influences on present day research in commutative algebra come from the pervading use of homological algebra, and from the ever growing demand and sophistication of computational methods.
		Special attention will be paid to presentations of new geometric ideas that could have a potential impact on research in commutative algebra.
	www-fourier.ujf-grenoble.fr /CONGRES/Morales01/indexgb.html (137 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		Our goal is to show that * such simplicial algebras* can be given a suitably rigid structure in the homotopy cat* egory, which then allows us to bring in methods from commutative* algebra.
		Theorem A provides the means to import in methods from commutative algebra, m* *ost notably localizations and completions.
		Suppose A is a simplicial commutative R-algebra, with R a Noet* *her- ian ring.
	www.math.purdue.edu /research/atopology/Turner/Noetherian.txt (1833 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.
		Examples of news include, but are not restricted to, announcements of awards being made to commutative algebraists and photos from conferences being posted.
		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.
	www.commalg.org (412 words)

	AN INTRODUCTION TO COMMUTATIVE ALGEBRA
		Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure.
		It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry.
		It is also a convenient reference for researchers who use basic commutative algebra.
	www.worldscibooks.com /mathematics/5617.html (147 words)

	››› buch.de - bücher - versandkostenfrei - Elements of Mathematics. Commutative Algebra. Chapters ...
		Mehr über: Algebra, algebraic geometry, Algebraische Geometrie, geometry, Geometrie / Algebraische Geometrie, Kommutation - kommutativ, kommutativ (Kommutation), Kommutative Algebra, commutative algebra, arithmetical, divisors, Mathematik; Handbuch/Lehrbuch, Algebra - General
		This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'.
		It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry.
	www.buch.de /buch/03074/232_elements_of_mathematics__commutative_algebra__chapters_1___7__band_chapt_1_7.html (407 words)

	Algebra Homework Help, Algebra Solvers, Free Math Tutors
		Algebra, math homework solvers, lessons and free tutors online.Pre-algebra, Algebra I, Algebra II, Geometry, Physics.
		Our 643 algebra tutors solved 68683 problems submitted by 18040 registered students, wrote 353 lessons, 140 solvers, to be seen by thousands!
		Click here to learn about algebra tutoring and how to promote your math website or a book.
	www.algebra.com (497 words)

	Amazon.com: Commutative Algebra I (Graduate Texts in Mathematics): Books: Oscar Zariski,Pierre Samuel,I.S. Cohen (Site not responding. Last check: 2007-11-02)
		Commutative Ring Theory (Cambridge Studies in Advanced Mathematics) by H.
		Commutative Algebra : with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud
		Homomorphic mappings of rings into fields are very common in commutative algebra and in its applications.
	www.amazon.com /exec/obidos/tg/detail/-/0387900896?v=glance (554 words)

	Books on Algebra (Site not responding. Last check: 2007-11-02)
		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 rest of the book is also quite interesting, but a little too specialized for a beginning algebra student.
	www.math.hawaii.edu /~lee/algebra/references.html (553 words)

	Algebraic Geometry, Commutative Algebra and Combinatorics -- Erice 2001, NATO Advanced Workshop
		The workshop in Erice will address a wide range of new developments in classical Algebraic Geometry such as curves and their moduli, surfaces, higher dimensional varieties, vector bundles, and toric varieties.
		A special focus will be on exterior algebra methods which have recently grown in importance in Algebraic Geometry, Commutative Algebra, and Combinatorics, and their computational aspects (Bernstein-Gel'fand-Gel'fand correspondence, Beilinson monad, theory of Chow forms and resultants, algebraic shifting, free resolutions over the exterior algebra, linear syzygies, hyperplane arrangements,...)
		Splendid beaches are to be found within about an hour's drive from Erice at San Vito Lo Capo, Scopello and Cornino.
	www.math.sunysb.edu /~sorin/Erice-2001 (542 words)

	››› buch.de - bücher - versandkostenfrei - Computational Commutative Algebra 1. - Lorenzo ...
		The book can be used by teachers and students alike as a comprehensive guide to both the theory and the practice of Computational Commutative Algebra.
		It has been made as self-contained as possible, and thus is ideally suited as a textbook for graduate or advanced undergraduate courses.
		The computational aspects of the tutorials can be carried out with the computer algebra system CoCoA, an introduction to which appears in an appendix.
	www.buch.de /buch/03089/233_computational_commutative_algebra_1_.html (411 words)

	Book: A Singular Introduction to Commutative Algebra
		The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.
		It is followed by the central concepts of commutative algebra such as integral closure, dimension theory, primary decomposition, Hilbert function, completion, flatness and homological algebra.
		An appendix is devoted to algebraic geometry to show how geometric problems can be understood using commutative algebra.
	www.singular.uni-kl.de /Singular-book.html (251 words)

	Mathematical Sciences Research Institute - Commutative Algebra: Interactions with Homological Algebra and ... (Site not responding. Last check: 2007-11-02)
		Commutative Algebra: Interactions with Homological Algebra and Representation Theory
		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.
	www.msri.org /calendar/workshops/WorkshopInfo/199/show_workshop (147 words)

	Commutative Algebra
		The Magma facility for commutative rings allows the user to define any ring, starting from the ring of integers, by repeatedly applying the four basic constructions: transcendental extension, quotient by an ideal, localization, and completion.
		Rings derived from a polynomial ring will be considered in this section, while fields, their orders and valuation rings will be presented in the following section.
		The fundamental tools on which most machinery for computational (commutative) ring theory is based include factorization of elements in a UFD, the efficient construction of standard bases for ideals and the factorization of ideals.
	magma.maths.usyd.edu.au /magma/Features/node132.html (119 words)

	Faculty groups at CUNY
		Schoutens, Hans: algebraic model theory, commutative algebra, algebraic geometry
		Szpiro, Lucien: (Distinguished Professor), commutative algebra, diophantine geometry, arithmetic algebraic geometry
		Szpiro, Lucien: commutative algebra, diophantine geometry, arithmetic algebraic geometry
	math.gc.cuny.edu /faculty/facultygroups.html (503 words)

	Commutative Algebra Seminar (Site not responding. Last check: 2007-11-02)
		Abstract: Levy and Klingler have studied which rings can have the structure of all indecomposable modules and their direct sum behaviour described without having to describe the module structure of all indecomposable modules over all finitely generated algebras at the same time.
		There is one open case in their theory, and Klingler understands this as a canonical form matrix problem.
		Paul Roberts, The commutativity of intersection with divisors.
	www.math.utah.edu /~spiroff/seminar (1258 words)

	MAT4200 - Commutative algebra (Site not responding. Last check: 2007-11-02)
		The course is a comprehensive introduction to algebra.
		It is meant to give students a foundation for further studies in algebra and algebraic geometry.
		Students who are admitted to study programmes or individual courses at UiO must each semester register which courses and exams they wish to sign up for by registering a study plan in StudentWeb.
	www.uio.no /studier/emner/matnat/math/MAT4200/index-eng.xml (244 words)

	Algebraic Geometry and Commutative Algebra - Department of Mathematics - University of Notre Dame
		Algebraic Geometry and Commutative Algebra - Department of Mathematics - University of Notre Dame
		Seminars related to Algebraic Geometry and Commutative Algebra
		It is number 88 on the campus map.
	www.nd.edu /%7Emathwww/research/algebra_geom.shtml (130 words)

	leuschke.org :: About/Contact
		September 21—22, Ithaca NY for the Route 81 Conference Commutative Algebra and Algebraic Geometry
		July 5—11, Buşteni, Romania for Homological and Combinatorial Aspects of Commutative Algebra
		May 21—28, Luminy France for CIRM workshop on Commutative Algebra and Interactions with Algebraic Geometry
	www.leuschke.org /About/Contact (307 words)

	Summer 2004 VIGRE Mini-courses
		During the past 30 years, the homological conjectures and related questions have had a significant impact on the development of commutative algebra.
		This area of research remains a rich one and is as influential today in the development of commutative algebra as it was decades ago.
		The aim of the mini-course was to introduce graduate students with some background in commutative algebra and young researchers to this area of research.
	www.math.utah.edu /vigre/minicourses/2004.html (545 words)

	Amazon.com: Undergraduate Commutative Algebra (London Mathematical Society Student Texts): Books: Miles Reid,J. W Bruce (Site not responding. Last check: 2007-11-02)
		In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry.
		In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory.
		This book is ideal for anyone seeking a primer on commutative algebra.
	www.amazon.com /exec/obidos/tg/detail/-/0521458897?v=glance (964 words)

	Combinatorial Commutative Algebra
		Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics.
		This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings.
		The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes.
	www.math.umn.edu /~ezra/cca.html (255 words)

	[No title]
		The purpose is for recent Ph.D.s and graduate students in the field to meet experienced researchers, to learn about recent developments in commutative algebra, to exchange ideas with one another, and to develop collaborations for future research.
		Plus, it gives us in the commutative algebra community a wonderful opportunity to celebrate the many important contributions of Roger and Sylvia Wiegand.
		The primary topics will be aspects of representation theory, homological algebra, computational algebra, and ideal theory that interact with commutative algebra.
	dreadnought.uta.edu /~dave/WiegandFest.html (226 words)

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