21. Singular Manual: Commutative Algebra D.4 commutative algebra. D.4.1 algebra_lib, procedures for computing with algebrasand maps. D.4.2 elim_lib, procedures for elimination, saturation and blowing up. http://www.singular.uni-kl.de/Manual/2-0-3/sing_523.htm

D.4 Commutative algebra D.4.1 algebra_lib procedures for computing with algebras and maps D.4.2 elim_lib procedures for elimination, saturation and blowing up D.4.3 homolog_lib procedures for homological algebra D.4.4 mprimdec_lib procedures for primary decomposition of modules D.4.5 mregular_lib procedures for Castelnuovo-Mumford regularity D.4.6 normal_lib procedure for normalization D.4.7 primdec_lib procedures for primary decomposition D.4.8 primitiv_lib procedures for finding a primitive element D.4.9 reesclos_lib Rees Algebra and integral closure of an ideal D.4.10 intprog_lib Integer Programming D.4.11 toric_lib toric ideals User manual for Singular version 2-0-3, February 2002, generated by

22. Lisbon Conference On Commutative Algebra Translate this page http://www.math.ist.utl.pt/lcca/

No Frames... If you need information concerning the Conference use the e-mail below. lcca@math.ist.utl.pt Sep 15 2002

23. Lisbon Conference On Commutative Algebra Translate this page http://www.math.ist.utl.pt/~mike/conf/

No Frames... If you need information concerning the Conference use the e-mail below. lcca@math.ist.utl.pt Sep 15 2002

24. Commutative Algebra Seminar commutative algebra Seminar. Meetings.Category Science Math Algebra Research Groups......commutative algebra Seminar Spring 20002001 Hilbert functions and Blow-up Algebras. Informationon last semester's commutative algebra available here. http://www.math.iitb.ac.in/seminar/alg.html

Commutative Algebra Seminar Spring 2000-2001 Hilbert functions and Blow-up Algebras Venue : Room 105 : On Mondays at 4.00 pm February 5, 12, 26 Prof. S. R. Ghorpade Hilbert Functions of Determinantal Varieties March 5, 12, 19 Mr. A. V. Jayanthan Castelnuovo-Mumford Regularity and Blow-Up Algebras Abstract : The Goto-Shimoda theorem about Cohen-Macaulayness of the Rees algebras was generalized to an arbitrary ideal by a number of researchers. We shall present one of the simplest proofs of the generalized Goto-Shimoda theorem due to Johnston and Katz which appeared in the proceedings of the AMS. Effort will be made to present the proof so that it is accessible to people who know only basic theory of CM rings. April 2, 9, 16 Prof. Balwant Singh Hilbert functions, Lech's Inequality and Blowing Up Abstract : We state three open questions concerning inequailities between Hilbert functions of local rings. One of the questions compares the Hilbert function at a closed point with the one at the generic point. Another one is the Hironaka-Lech Conjecture comparing Hilbert functions under a flat local homomorphism. The third question compares the Hilbert function of a local ring with the Hilbert function of the fiber of a blowing-up with a normally flat center. We shall show that the first two questions are essentially equivalent and that an affirmative answer to the third question implies an affirmative answer to the first two. We shall also describe some cases in which the questions have been settled.

25. Commutative Algebra Seminar commutative algebra Seminar 20002001. Hilbert-Samuel Polynomials.Venue Room 105 In this year long seminar, we plan to present http://www.math.iitb.ac.in/seminar/alg_autumn00.html

Commutative Algebra Seminar : 2000-2001 Hilbert-Samuel Polynomials Venue : Room 105 In this year long seminar, we plan to present several recent papers and related papers on Hilbert-Samuel polynomials of ideals in Cohen-Macaulay local rings. The following are some of the main themes : Depths of blow up rings and Hilbert coefficients Local cohomology and Hilbert coefficients Hilbert coefficients under monoidal transforms Hilbert functions of Rees algebras Hilbert polynomials of complete ideals Bounds on Hilbert coefficients References: [1] For further information, please contact Prof. J.K. Verma October 10 J. K. Verma Hilbert coefficients and depth of the tangent cone III October 10 A. V. Jayanthan Introduction to Hilbert-Samuel Polynomials IV October 3 J. K. Verma Hilbert coefficients and depth of the tangent cone II October 3 A. V. Jayanthan Introduction to Hilbert-Samuel Polynomials III September 26 J. K. Verma Hilbert coefficients and depth of the tangent cone I September 26 A. V. Jayanthan

26. Commutative Algebra -- From MathWorld commutative algebra, Let A denote an algebra, so that A is a vector space overR and, Atiyah, M. F. and MacDonald, I. G. Introduction to commutative algebra. http://mathworld.wolfram.com/CommutativeAlgebra.html

Algebra Named Algebras Miscellaneous Algebras Commutative Algebra Let A denote an -algebra, so that A is a vector space over R and Now define where . An Associative -algebra is commutative if for all . Similarly, a ring is commutative if the multiplication operation is commutative, and a Lie algebra is commutative if the commutator A, B ] is for every A and B in the Lie algebra Abelian Group Commutative References Atiyah, M. F. and MacDonald, I. G. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, pp. 9-10, 1969. Cox, D.; Little, J.; and O'Shea, D. Ideals, Varieties, and Algorithms: An Introduction to Algebraic Geometry and Commutative Algebra, 2nd ed. New York: Springer-Verlag, 1996. Eisenbud, D. (Ed.). Commutative Algebra, Algebraic Geometry, and Computational Methods. Singapore: Springer-Verlag, 1999. Finch, S. "Zero Structures in Real Algebras." http://www.mathsoft.com/asolve/zerodiv/zerodiv.html Kreuzer, M. and Robbiano, L. Computational Commutative Algebra 1. Berlin: Springer-Verlag, 2000. MacDonald, I. G. and Atiyah, M. F.

27. Steps In Commutative Algebra - Cambridge University Press Introductory account of commutative algebra, aimed at students with a backgroundin basic algebra. Steps in commutative algebra. 2nd Edition. Rodney Y. Sharp. http://books.cambridge.org/0521646235.htm

28. Undergraduate Commutative Algebra - Cambridge University Press For those looking for an introduction to the area of commutative algebra, this bookopens all the right doors and provides a clarity of understanding that all http://books.cambridge.org/0521458897.htm

29. Conference : Combinatorial Commutative Algebra Conference on Combinatorial commutative algebra. June 27 29, 1997.This page has moved. Please use http//www.exp-math.uni-essen http://www.uni-essen.de/fb6/conference.html

Conference on : Combinatorial Commutative Algebra June 27 - 29, 1997 This page has moved. Please use : http://www.exp-math.uni-essen.de/~forscher/conference.html

30. Research Group: Commutative Algebra Research Project commutative algebra. Members of the group JürgenHerzog Email mat300@uni-essen.de Tel. +49 201 183-2422 http://www.uni-essen.de/~mat306/

Research Project: Commutative Algebra Members of the group: E-mail : mat300@uni-essen.de Tel. : +49 201 183-2422 Attila Wiebe E-mail : attila.wiebe@uni-essen.de Tel. : +49 201 183-4114 Xinxian Zheng E-mail : xinxian.zheng@uni-essen.de Tel. : +49 201 183-4114 Naser Zamani E-mail : naser.zamani@uni-essen.de Tel. : +49 201 183-3923 Recent Preprints: Ideals of fiber type and polymatroids; (PS document) Monomial Ideals whose Powers have a linear resolution; (PS document) Multiplicities of Monomial Ideals; (PS document) Xinxian Zheng Resolutions of Facet Ideals; (PS document) (PS document) Poincare series of resolutions of surface singularities; (PS document) Koszul modules; (PS document) On the Ext-modules of ideals of Borel type; (PS document) Castelnuovo-Mumford regularity of simplicial semigroup rings with isolated singularity; (PS document) Approximations of generalized Cohen-Macaulay modules; (PS document) Discrete Polymatroids; (PS document) Castelnuovo-Mumford regularity of products of ideals; (PS document) Sequentially Cohen-Macaulay modules and local cohomology; (PS document) Resolutions by mapping cones;

31. COMMUTATIVE ALGEBRA NextPrev Right Left Up Index Root commutative algebra. Chapters.IDEAL THEORY AND GRÖBNER BASES. AFFINE ALGEBRAS. MODULES OVER AFFINE ALGEBRAS. http://magma.maths.usyd.edu.au/magma/htmlhelp/part10.htm

[Next] [Prev] [Right] [Left] ... [Root] COMMUTATIVE ALGEBRA Chapters AFFINE ALGEBRAS MODULES OVER AFFINE ALGEBRAS

32. Commutative Algebra next up previous Next Multivariate Polynomial Rings HB Up V2.7 ReleaseNotes Previous Local (including padic) Rings. commutative algebra. http://magma.maths.usyd.edu.au/magma/ReleaseNotes/rel27/node37.html

Next: Multivariate Polynomial Rings [HB Up: V2.7 Release Notes Previous: Local (including p-adic) Rings Commutative Algebra Multivariate Polynomial Rings [HB 50] Affine Algebras (New Chapter) [HB 51]

33. 13P: Computational Aspects Of Commutative Algebra 13P Computational aspects of commutative algebra. For now this page is largely aplaceholder; more information is on the parent page for commutative algebra. http://www.math.niu.edu/~rusin/known-math/index/13PXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 13P: Computational aspects of commutative algebra Introduction Perhaps the title makes it clear what this section is! For now this page is largely a placeholder; more information is on the parent page for commutative algebra History Applications and related fields The computational tools described on this page are used in other areas, particularly algebraic geometry and its subfields (e.g. one can compute the envelope of a curve ). Roughly speaking we have included here the comments which are best exemplified with varieties of dimension zero (finite sets of points) and in section 14 the comments which involve more geometry than computation. Computation in polynomial rings overlaps 12F: Field extensions (Galois theory). In particular, look there for computational questions involving the factorization of univariate polynomials. There have been a number of applications to topics in robotics and the motions of linked systems See Also 68W30 Subfields Polynomials, factorization, See also 12Y05

34. 13: Commutative Rings And Algebras A commutative algebra is a commutative ring which contains a field (usuallyas a subring over which the entire ring is finitelygenerated). http://www.math.niu.edu/~rusin/known-math/index/13-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 13: Commutative rings and algebras Introduction Commutative rings and algebras are sets like the set of integers, allowing addition and (commutative) multiplication. 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. A commutative ring is a set endowed with two binary operations "+" and "*" subject to familiar associative, commutative, and distributive laws. (It is usually but not universally assumed that the rings contain an identity element "1" for multiplication.) Examples include the rings of integers in algebraic number fields; here, the interest is number-theoretic: common questions concern factorization and the class group, the action of the Galois group, and the structure of the group of units. A commutative algebra is a commutative ring which contains a field (usually as a subring over which the entire ring is finitely-generated). Examples include coordinate rings of algebraic varieties, that is, quotients of polynomial rings over a field; here, the interest is geometric: how are the local rings different at singular points, and how do subvarieties intersect? In some sense the theory of commutative rings and algebras can be seen as the search for common features of these two classes of examples, and the effort to explain features of a general commutative ring as being like these two types. We can clarify these fields of inquiry by reviewing the subfields of section 13.

35. 2003 Joint Summer Research Conference On Commutative Algebra: Presentations By Y of 2003 Joint Summer Research Conference on CommutativeAlgebra Presentations by Young Researchers....... http://www.ams.org/meetings/src-herzog.html

pop@ams.org Commutative Algebra: Presentations by Young Researchers Sunday, July 20 - Thursday, July 24 Craig Huneke , University of Kansas Roger L. Wiegand , University of Nebraska The goal of the conference is to bring together young researchers in several areas of commutative algebra in order to provide a showcase for important new ideas and to encourage collaboration among participants. All research talks will be given by mathematically young researchers, primarily those no more than two or three years beyond the Ph.D., and graduate students in their final year of study. The conference will focus on the following topics: (1) homological methods in commutative algebra, (2) characteristic methods and tight closure, (3) combinatorics and commutative algebra, and (4) representation theory of local rings. Each topic will be introduced by an expository talk, and informal discussions will follow the research talks. The following individuals have at least tentatively accepted invitations to give research talks: Holger Brenner C-Y. Jean Chan

36. Commutative Algebra And Geometry commutative algebra and Geometry. Month March 2003 Date March 29April3. Name commutative algebra and Geometry. Location Banff http://www.ams.org/mathcal/info/2003_mar29-apr3_banff.html

Commutative Algebra and Geometry Month: March 2003 Date: March 29April 3 Name: Commutative Algebra and Geometry Location: Banff International Research Station, Banff, Alberta, Canada. Organizers M. Green (IPAM), J. Herzog (Univ. Essen), B. Sturmfels (Univ. Calif., Berkeley). Information http://www.pims.math.ca/birs/

37. KU Mathematics: Algebra/Algebraic Geometry Algebra/Algebraic Geometry. Algebra/Algebraic Geometry. Craig Huneke CommutativeAlgebra, Algebraic Geometry; Daniel Katz commutative algebra; http://www.math.ukans.edu/research/algebra.html

Algebra/Algebraic Geometry Algebra/Algebraic Geometry Craig Huneke: Commutative Algebra, Algebraic Geometry Daniel Katz: Commutative Algebra Jeffery Lang: Commutative Algebra Graham Leuschke: Commutative Algebra Satyagopal Mandal: Commutative Algebra Bangere Purnaprajna: Algebraic Geometry Adela Vraciu: Commutative Algebra For further research, teaching, and other information visit the Group's Page Please direct comments to webcomments@math.ukans.edu Last modified: Mar 28, 2002

38. Commutative Algebra & Algebraic Geometry http://www.math.ukans.edu/caag/

39. KLUWER Academic Publishers | Approximation Theorems In Commutative Algebra Books » Approximation Theorems in commutative algebra. Approximation Theoremsin commutative algebra Classical and Categorical Methods. Add to cart. http://www.wkap.nl/prod/b/0-7923-1948-6

Title Authors Affiliation ISBN ISSN advanced search search tips Books Approximation Theorems in Commutative Algebra Approximation Theorems in Commutative Algebra Classical and Categorical Methods Add to cart by J. Alajbegovic University of Ostava, Czech Republic Book Series: MATHEMATICS AND ITS APPLICATIONS East European Series Volume 59 Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc. Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d -groups. Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic. For researchers and graduate students of commutative algebra, category theory, as well as applications of logic. Contents Kluwer Academic Publishers, Dordrecht

40. Commutative Algebra Seminar, University Of Utah commutative algebra Seminar. The seminar will usually meet on Fridays at305 pm in JWB 208. January 25, 2002. Florian Enescu Multiplicities http://www.math.utah.edu/~singh/seminar.html

Commutative Algebra Seminar The seminar will usually meet on Fridays at 3:05 pm in JWB 208. January 25, 2002. Florian Enescu Multiplicities and tight closure of parameter ideals (after S. Goto and Y. Nakamura). I February 1, 2002. Florian Enescu Multiplicities and tight closure of parameter ideals (after S. Goto and Y. Nakamura). II March 15, 2002. Greg Piepmeyer Zariski's main theorem. I March 22, 2002. Greg Piepmeyer Zariski's main theorem. II March 29, 2002. Catalin Ciuperca, University of California, Riverside Generalized Hilbert coefficients. April 19, 2002. Anurag Singh Rings of invariants in positive characteristic. I April 26, 2002. Anurag Singh Rings of invariants in positive characteristic. II Fall 2001 September 7, 2001. Florian Enescu Flat base change problems in tight closure theory. I September 21, 2001. Florian Enescu Flat base change problems in tight closure theory. II September 27, 2001. Kazuhiko Kurano, Tokyo Metropolitan University Numerical equivalence on Chow groups of local rings. I September 28, 2001. Kazuhiko Kurano, Tokyo Metropolitan University

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