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Commutative Algebra: more books (100)

Computational Algebraic Geometry and Commutative Algebra (Symposia Mathematica)
An Introduction to Group Rings (Algebra and Applications) by César Polcino Milies, S.K. Sehgal, 2008-05-27
Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics) by Patrice Tauvel, Rupert W. T. Yu, 2010-11-30
A Field Guide to Algebra (Undergraduate Texts in Mathematics) by Antoine Chambert-Loir, 2010-11-02
Introduction to Commutative Algebra and Algebraic Geometry by Ernst Kunz, 1984-01-01
Gröbner Bases: A Computational Approach to Commutative Algebra (Graduate Texts in Mathematics) (v. 141) by Thomas Becker, Volker Weispfenning, 1993-04-08
Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups (Universitext) by Alexander J. Hahn, 1993-12-17
Algebra II: Noncommutative Rings. Identities (Encyclopaedia of Mathematical Sciences) (v. 2)
Multiplicative Ideal Theory in Commutative Algebra: A Tribute to the Work of Robert Gilmer
The Use of Ultraproducts in Commutative Algebra (Lecture Notes in Mathematics) by Hans Schoutens, 2010-08-02
Algebras, Rings and Modules: Volume 1 (Mathematics and Its Applications) by Michiel Hazewinkel, Nadiya Gubareni, et all 2010-11-02
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) by David A. Cox, John Little, et all 2007-02-14
Graduate Algebra: Commutative View by Louis Halle Rowen, 2006-07-26
Shift-invariant Uniform Algebras on Groups (Monografie Matematyczne) by Suren A. Grigoryan, Toma V. Tonev, 2006-06-30

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Commutative Algebra - Local Rings
Let R be any (possibly noncommutative) ring and let G be any group. Then the group ring R G is defined to be the set of formal linear combinations Sum;
http://crypto.stanford.edu/pbc/notes/commalg/local.xhtml

Extractions: We call a ring R local if R has exactly one maximal ideal M . In this case, we call A M the residue field of R . A ring with only finitely many maximal ideals is called semi-local Example: Any field F is local and F is its own residue field. Let R be any (possibly noncommutative) ring and let G be any group. Then the group ring R G is defined to be the set of formal linear combinations g G g g where every g R , and only finitely many g are nonzero, with componentwise addition: g g g g g g g and convolution product: g G g g h G h h k G g h k g h k Take the cyclic group of order 2 C x x . Then C x x . This is a local ring with maximal ideal x and its residue field is isomorphic to Let F be a field of characteristic p , that is sum i p , and let G be any abelian p -group , that is, the order of every element of G is a power of p . Then F G is local with unique maximal ideal M g g g with residue field isomorphic to F . 3. The ring a b a b b is local with residue field . The ring a b a b b b is semi-local. We can continue in this fashion: by taking the first n primes we can construct a semi-local ring with exactly n maximal ideals. 4. The ring
2010 Research In Teams: Derived Category Methods In Commutative Algebra II | Ban
Derived category methods have proved to be very successful in ring theory, in particular in commutative algebra. Evidence is provided by cite{AJL97,bour10,
http://www.birs.ca/events/2010/research-in-teams/10rit158

Extractions: Lars Christensen (Texas Tech University) The book offers a systematic development of hyperhomological algebra. This includes the construction of the derived category of a general (associative) ring and a careful study of the functors of importance in ring theory. To demonstrate the strength and utility of the theory, and to motivate the choice of topics, the book includes an extensive course in central homological aspects of commutative ring theory. This part includes many recent results, which were discovered by means of derived category methods, and gives valuable new insight into the theory of commutative rings and their modules. Objective Authors Apart from the need for such a book, our motivation for actually writing it has two sources. It stems from repeated urgings from colleagues and from personal desires to see a presentation of the theory that not only makes the case for derived category methods but also provides a comprehensive and coherent reference for the theory and its applications in commutative algebra. The applicants maintain active research programs in commutative algebra. These programs rely heavily on derived category methods - and more advanced techniques of differential graded algebra
Introduction To Commutative Algebra | EHow.com
Sep 11, 2009 Introduction to Commutative Algebra. Algebra is simply logic. Algebraic reasoning is based on consistencies and rules that apply when
http://www.ehow.com/about_5402966_introduction-commutative-algebra.html

Extractions: Home Education Math Education ... Introduction to Commutative Algebra By Samantha Hanly eHow Contributor updated: September 11, 2009 I want to do this! What's This? Algebra is simply logic. Algebraic reasoning is based on consistencies and rules that apply when dealing with numbers or numeric values. Learning and comprehending the properties of numbers and how they behave and interact make memorization less important in the study of algebra. When the basic laws of algebra logic are understood and applied, then what may look like complicated mathematical equations become much easier to solve. One of rules of algebra is the commutative property. Merriam-Webster's online dictionary defines "commutative" as an adjective that describes something that shows commutation.

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