Geometry.Net - Pure_And_Applied_Math: Commutative Algebra

Math 676. Commutative Algebra
Math 676. commutative algebra terms offered, credit hours, prerequisites, andcourse description. Math 676. commutative algebra. Offered F odd years.
http://www.math.byu.edu/Programs/676.html
Introduction To Commutative Algebra
Introduction to commutative algebra, Introduction to commutative algebra byAuthors IG MacDonald,Michael Francis Atiyah Released December, 1994 ISBN
http://www.wkonline.com/a/Introduction_to_Commutative_Algebra_0201407515.htm

Extractions: This is a fantastic book in every way but one. Perseus Books has done such a terrible job printing it that I am returning my copy. It looks and feels worse than any book I have ever held in my hands. The paper is cheaper than any book I have on my shelf. I can see an empty spot in the glue on the binding. The text itself looks like a second generation photocopy. All of this is a terrible disappointment to me, because everyone I have talked to has loved the content of the book, and I was expecting a good, strong paperback that I could keep for thirty years. This doesnt feel like itll last thirty days. I cant recommend that anyone buy this book. Perhaps if you could get a cheap used copy it would be worth it, but sixty dollars? No. Get something else.
Commutative Algebra With A View Toward Algebraic Geometry (Graduate Texts In Mat
commutative algebra With a View Toward Algebraic Geometry (Graduate Texts in Mathematics,Vol 150), commutative algebra With a View Toward Algebraic Geometry
http://www.wkonline.com/a/Commutative_Algebra_With_a_View_Toward_Algebraic_Geome

Extractions: If one is interested in taking on a thorough study of algebraic geometry, this book is a perfect starting point. The writing is excellent, and the student will find many exercises that illustrate and extend the results in each chapter. Readers are expected to have an undergraduate background in algebra, and maybe some analysis and elementary notions from differential geometry. Space does not permit a thorough review here, so just a brief summary of the places where the author has done an exceptional job of explaining or motivating a particular concept: (1) The history of commutative algebra and its connection with algebraic geometry, for example the origin of the concept of an "ideal" of a ring as generalizing unique factorization.
Math 252: Commutative Algebra And Algebraic Geometry
Math 252 commutative algebra and Algebraic Geometry (Spring 2003). This is a basicintroductory course in commutative algebra for first year graduate students.
http://www.math.duke.edu/graduate/courses/spring03/math252.html

Extractions: Bill Pardon This is a basic introductory course in commutative algebra for first year graduate students. Commutative algebra forms the foundation on which algebraic geometry and algebraic number theory are built, however it is an important course for all students interested in studying geometry, topology, and mathematical physics. Topics: Extension and contraction of ideals, modules of fractions, primary decomposition, integral dependence, chain conditions, affine algebraic varieties, Dedekind domains, completions. Weekly homework assignments graded by the instructor. Math 251 (basic algebra) is a prerequisite. Return to: Course List Math Graduate Program Department of Mathematics Duke University Last modified: 31 October 2002
Math 252: Commutative Algebra And Algebraic Geometry
.This is a basic, introductory course in commutative algebra.Math 252 commutative algebra and Algebraic Geometry (Spring 2002). Instructor.
http://www.math.duke.edu/graduate/courses/spring02/math252.html

Extractions: Andreas Rosenchon This is a basic, introductory course in commutative algebra. Commutative algebra forms the foundation on which Algebraic Geometry and Algebraic Number Theory are built. As there is much more basic commutative algebra than can be covered in a one semester course, some selection of topics is necessary. Since Math 252 is a prerequisite for the Math 273 (Algebraic Geometry), but not for the Algebraic Number Theory course, there will be a strong bias towards classical algebraic geometry and away from number theory. A list of notions from algebraic geometry which will be covered is included below. We will restrict attention to algebraic varieties over algebraically closed fields. Mostly we will work with the category of affine varieties, although projective varieties will be touched upon. The Zariski topology on affine space, affine varieties, Noetherian topological spaces, Krull dimension, irreduciblity, polynomial maps between affine varieties, closed embeddings, dominant maps, product varieties, principal open subsets, affine algebraic groups, tori, affine toric varieties, the tangent space, finite maps, closed maps, quotients by finite group actions, constructible sets, images of polynomial maps, bounds on dimensions of intersections, the singular locus, open maps, flat maps, dimensions of fibers of polynomial maps, projective varieties, Hilbert functions, Bezout's theorem for intersection with a projective hypersurface, tangent cones, foundations of the theory of divisors on a smooth complex analytic space or variety (divisors will only be introduced in the algebraic geometry course; we just do the commutative algebra needed to get the theory going).
MathGroup Archive: October 1994 Non-commutative Algebra
noncommutative algebra. Date Tue, 18 Oct 1994 095836 +0100 (MET). Sir, Iam looking for a way to do some calculations in a non-commutative algebra.
http://forums.wolfram.com/mathgroup/archive/1994/Oct/msg00013.html

Extractions: January February March April ... Author Index Sir, I am looking for a way to do some calculations in a non-commutative algebra. I want to do things in which A . x . B = A . B . x = x . A . B but where A and B are non-commutative. Are there packages available ? Thanks ============================================================================== Marnix Van Daele Universiteit Gent Vakgroep Toegepaste Wiskunde en Informatica Krijgslaan 281 - Gebouw S9 B9000 Gent (Belgium) tel. 32-(0)9-264.48.09 fax. 32-(0)9-264.49.95 ============================================================================== Prev by Date: intersection of two graphics Next by Date: Duplicates from MathGroup Prev by thread: intersection of two graphics Next by thread: linespacing and subscripts in graphics
Webserver
next contents index Next Contents. 60pt -45pt. CALI A REDUCE Packagefor commutative algebra Version 2.1. Hans-Gert Gräbe Universität
http://www.rrz.uni-koeln.de/REDUCE/cali/cali.html
Commutative Algebra
next previous up top index search for commutative algebra. integralClosure;primaryDecomposition; symmetricAlgebra next previous up top index
http://www.math.uiuc.edu/Macaulay2/Manual/1826.html
Commutative Algebra And Algebraic Geometry [SS2003]
commutative algebra and Algebraic GeometrySS2003. Prof. Franz Winkler.commutative algebra and Algebraic Geometry. Time and room.
http://www.risc.uni-linz.ac.at/courses/ss2003/CAAG/

Extractions: Prof. Franz Winkler Commutative Algebra and Algebraic Geometry Time and room Lecture: Tue 13:45-15:15 in P004, Fri 12:00-13:30 in T711 Exercises: Tue 15:30-16:15 in KG416 first lecture: March 11 Short Description Algebraic geometry is an old and intensively studied area of mathematics. It is concerned with geometric objects which can be described as the zero locus of polynomial equations, i.e. algebraic curves, surfaces, and varieties in higher dimension. Nowadays such algebraic curves and surfaces are of high importance in computer aided geometric design, computer vision, cryptography, and other application areas. The algebraic theory which allows us to compute with such algebraic varieties is the theory of polynomials or commutative algebra. Polynomial ideals, radicals, polynomial and rational functions and mappings and the like lend themselves to computational methods from computer algebra. In this course we will examine the relation between the algebraic theory of polynomial ideals and the geometry of curves, surfaces, and algebraic varieties.
Advanced Example 2: Implementing A Non-commutative Algebra
Advanced example 2 implementing a noncommutative algebra. We needto understand how to simplify expressions in Yacas, and the best
http://yacas.sourceforge.net/codingchapter8.html

Extractions: We need to understand how to simplify expressions in Yacas, and the best way is to try writing our own algebraic expression handler. In this chapter we shall consider a simple implementation of a particular non-commutative algebra called the Heisenberg algebra. This algebra was introduced by Dirac to develop quantum field theory. We won't explain any physics here, but instead we shall to delve somewhat deeper into the workings of Yacas. Suppose we want to define special symbols A(k) and B(k) that we can multiply with each other or by a number, or add to each other, but not commute with each other, i.e. A(k)*B(k)!=B(k)*A(k) . Here k is merely a label to denote that A(1) and A(2) are two different objects. (In physics, these are called "creation" and "annihilation" operators for "bosonic quantum fields".) Yacas already assumes that the usual multiplication operator " " is commutative. Rather than trying to redefine , we shall introduce a special multiplication sign " " that we shall use with the objects A(k) and B(k) ; between usual numbers this would be the same as normal multiplication. The symbols
Commutative Algebra Seminar At IMUJ (1996/97)
commutative algebra SEMINAR. dr hab. Ludwik Dru¿kowski dr hab. Kamil RusekIMUJ, Kraków ul. Reymonta 4, room 502 Wednesdays, 1230 1400.
http://www.im.uj.edu.pl/~gurycz/seminaria/comalg9697.html

Extractions: We want to study the relationship between an affine variety V and the structure of a Lie algebra L of derivations of V's coordinate ring A. First we check the connection beetween Lie ideals of L and integral ideals of A. To get some intuition we give examples of subalgebras of L, integral ideals of A (D-ideals), modular and non-modular ideals of L. Then following D.A. Jordan, A. Seidenberg and T. Siebert we prove that V is smooth if and only if L is simple.
COMMUTATIVE ALGEBRA
commutative algebra Proceedings of the Workshop ICTP, Trieste, Italy 14 25September 1992 edited by A Simis (Univ. Federal da Bahia), NV Trung (Inst.
http://www.wspc.com/books/mathematics/2274.html

Extractions: In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools. One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results. At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra such as deformation, linkage, algebraic tori and determinantal rings, etc. This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.
Elementary Aspects Of Constructive Commutative Algebra - Forsman (ResearchIndex)
are described in most classical textbooks on commutative algebra 17, 20,25, 32 ffl Some references for GB are 3, 10, 14, 15, 16, 29, 33.
http://citeseer.nj.nec.com/forsman92elementary.html

Extractions: Abstract: hodes effectives et bornes de complexit'e. PhD thesis, ' Ecole Polytechnique, 1990. [60] F. Ollivier. Canonical bases: Relations with standard bases, finiteness conditions and application to tame automorphisms. In T. Mora and C. Traverso, editors, Effective Methods in Algebraic Geometry, volume 94 of Progress in Mathematics, pages 379400. Birkhauser, 1991. From the Symposium MEGA 90, held at Castiglioncello, Italy, 1990. [61] F. Pauer and M. Pfeifhofer. The theory of Grobner bases.... (Update)
MC440 Commutative Algebra
MC440 commutative algebra. MC440 commutative algebra. Credits 20, The developmentof understanding of the abstract method within commutative algebra.
http://www.mcs.le.ac.uk/Modules/Modules00-01/MC440.html
4.2.1 COMMUTATIVE ALGEBRADr Gardener16 Lectures MT
4.2.1.1 Reading List. 4.2.1 commutative algebraDr Gardener16 lectures MT. 4.2.1.1Reading List. Atiyah and Macdonald Introduction to commutative algebra.
http://www.maths.ox.ac.uk/teaching/synopses/2001/mfoc-01/node19.html
Algebraic Geometry And Commutative Algebra (Joseph Bernstein)
0366.4148.01 Algebraic Geometry and commutative algebra 1. Society, Lecture NotesSeries, v.172). MF Atiyah, IG.MacDonald, Introduction to commutative algebra.
http://www.math.tau.ac.il/~bernstei/courses/agf00/ag.html
Algebraic Geometry And Commutative Algebra (Joseph Bernstein)
0366.4148.01 Algebraic Geometry and commutative algebra 1. Lecturer JosephBernstein School of Mathematical Sciences, Fall Semester 2002/2003.
http://www.math.tau.ac.il/~bernstei/courses/agf02/ag.html
OUP USA: An Introductory Course In Commutative Algebra
by Subject $75.00 (04) 019853423X Add to My Basket 1998 In Stock S H StandardTable of Contents, An Introductory Course in commutative algebra AW CHATTERS
http://www.oup-usa.org/isbn/019853423X.html

Extractions: The authors provide a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. Their treatment combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields, which has important uses in other branches of science. Topics covered include rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups and finite fields. The material can serve equally well as a textbook for an entire course or as preparation for the further study of abstract algebra.
Mathematical Sciences, 21-715 Commutative Algebra
Graduate Courses. 21715 commutative algebra 12 units. Commutativeideal theory localization, prime spectrum, integral dependence
http://www.math.cmu.edu/grad/courses/21-715.html

Extractions: 12 units Commutative ideal theory: localization, prime spectrum, integral dependence, free and projective modules, primary decomposition, Krull dimension, fractional ideals, Dedekind domains, Hilbert finite basis theorem, Hilbert Nullstellensatz, affine algebraic varieties, coordinatization. Valuation theory: normed fields, completion, p-adic fields, Ostrowski's theorem, valuations, discrete valuations, Hensel's lemma, local fields. Prerequisite: Mathematical Sciences Home Mellon College of Science Carnegie Mellon University
21-715 Algebra II (Commutative Algebra)
21715 Algebra II (commutative algebra). Contents Will present some of thebasic facts of commutative algebra from the geometric point of view.
http://www.math.cmu.edu/users/rami/comalg.html

Extractions: 21-715 Algebra II (Commutative Algebra) Lecturer: Rami Grossberg Starting : Spring 1998, MWF 3:30 PM General: Contents: Will present some of the basic facts of commutative algebra from the geometric point of view. If time permits, I will discuss the theory of normed fields. Most of the course will be based on the following (very short) books: 1. M. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra 2. W. Fulton, Algebraic Curves The authors (of both books) claim that the books are based on undergraduate courses. Fulton mentions in the introduction to his book that he taught the contents of his book to graduate students in one week. Our pace will be slower than his! Prerequisites More information: Contact R. Grossberg WeH 6218 (ext. 8482); Email: Rami@ cmu.edu

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