Author: Publisher:
ISBN:
Category : Group rings
Languages : en
Pages : 98
Book Description
Skew Polynomial Rings, Group Rings and Related Topics
Author: Prime Ideals in Skew and $Q$-Skew Polynomial Rings
Author: K. R. GoodearlPublisher: Oxford University Press, USA
ISBN: 9781470400989
Category : MATHEMATICS
Languages : en
Pages : 118
Book Description
There has been continued interest in skew polynomial rings and related constructions since Ore's initial studies in the 1930s. New examples not covered by previous analyses have arisen in the current study of quantum groups. The aim of this work is to introduce and develop new techniques for understanding the prime ideals in skew polynomial rings $S=R[y;\tau, \delta]$, for automorphisms $\tau$ and $\tau$-derivations $\delta$ of a noetherian coefficient ring $R$. Goodearl and Letzter give particular emphasis to the use of recently developed techniques from the theory of noncommutative noetherian rings. When $R$ is an algebra over a field $k$ on which $\tau$ and $\delta$ act trivially, a complete description of the prime ideals of $S$ is given under the additional assumption that $\tau -1 \delta \tau = q\delta$ for some nonzero $q\in k$. This last hypothesis is an abstraction of behavior found in many quantum algebras, including $q$-Weyl algebras and coordinate rings of quantum matrices, and specific examples along these lines are considered in detail.
Skew Polynomial Rings and Overrings
Author: J. C. WilkinsonTopics in Group Rings
Author: Sudarshan K. SehgalPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 272
Book Description
The group ring KG of the group G over a commutative unital ring K comprises an attractive object of study. This is one of the few algebraic structures that allow for explicit computations. Several easily formulated questions are associated with this topic. Many interesting results have been obtained in this area by using deep results and techniques from group theory, ring theory, and number theory. Most of the results presented and techniques used have a number theoretic flavor. Aimed at advanced graduate students and research mathematicians in algebra.
An Introduction to Noncommutative Noetherian Rings
Author: K. R. GoodearlPublisher: Cambridge University Press
ISBN: 9780521545372
Category : Mathematics
Languages : en
Pages : 372
Book Description
This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.
Group Rings and Their Augmentation Ideals
Author: I.B.S. PassiPublisher: Springer
ISBN: 354035297X
Category : Mathematics
Languages : en
Pages : 144
Book Description
Classical Artinian Rings and Related Topics
Author: Yoshitomo BabaPublisher: World Scientific
ISBN: 9814287245
Category : Mathematics
Languages : en
Pages : 310
Book Description
Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since then, these classical artinian rings have continued to fascinate ring theorists with their abundance of properties and structural depth. In 1978, M Harada introduced a new class of artinian rings which were later called Harada rings in his honour. Quasi-Frobenius rings, Nakayama rings and Harada rings are very closely interrelated. As a result, from a new perspective, we may study the classical artinian rings through their interaction and overlap with Harada rings. The objective of this seminal work is to present the structure of Harada rings and provide important applications of this structure to the classical artinian rings. In the process, we cover many topics on artinian rings, using a wide variety of concepts from the theory of rings and modules. In particular, we consider the following topics, all of which are currently of much interest and ongoing research: Nakayama permutations, Nakayama automorphisms, Fuller's theorem on i-pairs, artinian rings with self-duality, skew-matrix rings, the classification of Nakayama rings, Nakayama group algebras, the Faith conjecture, constructions of local quasi-Frobenius rings, lifting modules, and extending modules. In our presentation of these topics, the reader will be able to retrace the history of artinian rings.
Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics
Author: Pramod M. AcharPublisher: American Mathematical Society
ISBN: 0821898523
Category : Mathematics
Languages : en
Pages : 296
Book Description
This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.
Groups, Rings, and Group Rings
Author: A. GiambrunoPublisher: American Mathematical Soc.
ISBN: 0821858254
Category : Mathematics
Languages : en
Pages : 283
Book Description
"This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28-August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed."--Publisher's website.
Skew Polynomial Rings and Nilpotent Derivations
Author: Theodorus Hermanus Maria SmitsPublisher:
ISBN:
Category : Rings (Algebra)
Languages : en
Pages : 80
Book Description