Quotient Rings and Embeddings of Noetherian Rings
Author : Anders Jensen
Publisher :
Page : 110 pages
File Size : 38,56 MB
Release : 1991
Category :
ISBN :
Author : Anders Jensen
Publisher :
Page : 110 pages
File Size : 38,56 MB
Release : 1991
Category :
ISBN :
Author : John Jim Papadopoulos
Publisher :
Page : 52 pages
File Size : 31,25 MB
Release : 1974
Category :
ISBN :
Author : K. R. Goodearl
Publisher : Cambridge University Press
Page : 372 pages
File Size : 11,16 MB
Release : 2004-07-12
Category : Mathematics
ISBN : 9780521545372
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.
Author : John C. McConnell
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 46,79 MB
Release : 2001
Category : Mathematics
ISBN : 0821821695
This is a reprinted edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics.
Author : Lance W. Small
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 11,15 MB
Release : 1987
Category : Mathematics
ISBN : 0821815253
". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.
Author : K. R. Goodearl
Publisher : Cambridge University Press
Page : 328 pages
File Size : 38,64 MB
Release : 1989
Category : Mathematics
ISBN : 9780521369251
Introduces and applies the standard techniques in the area (ring of fractions, bimodules, Krull dimension, linked prime ideals).
Author : Carl Faith
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 19,1 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642806341
VI of Oregon lectures in 1962, Bass gave simplified proofs of a number of "Morita Theorems", incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::! mod-B for two rings A and B. Morita's solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a similarity class [AJ in the Brauer group Br(k) of Azumaya algebras over a commutative ring k consists of all algebras B such that the corresponding categories mod-A and mod-B consisting of k-linear morphisms are equivalent by a k-linear functor. (For fields, Br(k) consists of similarity classes of simple central algebras, and for arbitrary commutative k, this is subsumed under the Azumaya [51]1 and Auslander-Goldman [60J Brauer group. ) Numerous other instances of a wedding of ring theory and category (albeit a shot gun wedding!) are contained in the text. Furthermore, in. my attempt to further simplify proofs, notably to eliminate the need for tensor products in Bass's exposition, I uncovered a vein of ideas and new theorems lying wholely within ring theory. This constitutes much of Chapter 4 -the Morita theorem is Theorem 4. 29-and the basis for it is a corre spondence theorem for projective modules (Theorem 4. 7) suggested by the Morita context. As a by-product, this provides foundation for a rather complete theory of simple Noetherian rings-but more about this in the introduction.
Author : Carolyn Anne Dean
Publisher :
Page : 118 pages
File Size : 27,87 MB
Release : 1986
Category : Associative rings
ISBN :
Author : A. V. Jategaonkar
Publisher : Cambridge University Press
Page : 341 pages
File Size : 27,80 MB
Release : 1986-03-13
Category : Mathematics
ISBN : 0521317134
This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.
Author : Bo T. Stenström
Publisher : Springer
Page : 328 pages
File Size : 20,5 MB
Release : 1975
Category : Categories (Mathematics).
ISBN :