An Introduction to Noncommutative Noetherian Rings

K.R. Goodearl, R.B. Warfield - Collection London Mathematical Society Student Texts

344 pages, parution le 15/09/2004 (2^eme édition)

Ajouter à une liste

Indisponible

Résumé

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.

Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory.

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.

L'auteur - K.R. Goodearl

K.R. Goodearl : University of California, Santa Barbara

Sommaire

A few Noetherian rings
Skew polynomial rings
Prime ideals
Semisimple modules, Artinian modules, and torsionfree modules
Injective hulls
Semisimple rings of fractions
Modules over semiprime Goldie rings
Bimodules and affiliated prime ideals
Fully bounded rings
Rings and modules of fractions
Artinian quotient rings
Links between prime ideals
The Artin-Rees property
Rings satisfying the second layer condition
Krull dimension
Numbers of generators of modules
Transcendental division algebras

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	K.R. Goodearl, R.B. Warfield
Collection	London Mathematical Society Student Texts
Parution	15/09/2004
Édition	2^eme édition
Nb. de pages	344
Format	15 x 23
Couverture	Broché
Poids	490g
Intérieur	Noir et Blanc
EAN13	9780521545372
ISBN13	978-0-521-54537-2