Commutative Algebra - Proceedings Of The Workshop

Commutative Algebra - Proceedings Of The Workshop
Author: Giuseppe Valla
Publisher: World Scientific
Total Pages: 330
Release: 1994-08-19
Genre:
ISBN: 9814551791

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.

Modules and Algebras

Modules and Algebras
Author: Robert Wisbauer
Publisher: CRC Press
Total Pages: 384
Release: 1996-05-15
Genre: Mathematics
ISBN: 9780582289819

Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.

Rings, Hopf Algebras, and Brauer Groups

Rings, Hopf Algebras, and Brauer Groups
Author: Stefaan Caenepeel
Publisher: CRC Press
Total Pages: 352
Release: 2020-09-29
Genre: Mathematics
ISBN: 1000153282

"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Abelian Groups and Noncommutative Rings: A Collection of Papers in Memory of Robert B. Warfield, Jr.

Abelian Groups and Noncommutative Rings: A Collection of Papers in Memory of Robert B. Warfield, Jr.
Author: László Fuchs
Publisher: American Mathematical Soc.
Total Pages: 408
Release: 1992
Genre: Mathematics
ISBN: 082185142X

This collection of research papers is dedicated to the memory of the distinguished algebraist Robert B. Warfield, Jr. Focusing on abelian group theory and noncommutative ring theory, the book covers a wide range of topics reflecting Warfield's interests and includes two articles surveying his contributions to mathematics. Because the articles have been refereed to high standards and will not appear elsewhere, this volume is indispensable to any researcher in noncommutative ring theory or abelian group theory. With papers by some of the major leaders in the field, this book will also be important to anyone interested in these areas, as it provides an overview of current research directions.

Invariants under Tori of Rings of Differential Operators and Related Topics

Invariants under Tori of Rings of Differential Operators and Related Topics
Author: Ian Malcolm Musson
Publisher: American Mathematical Soc.
Total Pages: 99
Release: 1998
Genre: Mathematics
ISBN: 0821808850

If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X) $ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k \times (k ) $. They give a precise description of the primitive ideals in $D(X) $ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X) $. The latter are of the form $B =D(X) /({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g} ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X/\!/G)$ is a simple ring.

Advances In Ring Theory - Proceedings Of The 4th China-japan-korea International Conference

Advances In Ring Theory - Proceedings Of The 4th China-japan-korea International Conference
Author: Jianlong Chen
Publisher: World Scientific
Total Pages: 335
Release: 2005-08-22
Genre: Mathematics
ISBN: 9814479705

The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the various areas of ring and module theory — ideal for researchers looking for a new or related field of study. Also included are original articles showing the trend of current research.