Localization of Noncommutative Rings
Author | : Jonathan S. Golan |
Publisher | : CRC Press |
Total Pages | : 352 |
Release | : 1975-01-01 |
Genre | : Mathematics |
ISBN | : 9780824761981 |
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Author | : Jonathan S. Golan |
Publisher | : CRC Press |
Total Pages | : 352 |
Release | : 1975-01-01 |
Genre | : Mathematics |
ISBN | : 9780824761981 |
Author | : Bruno J. Müller |
Publisher | : |
Total Pages | : 84 |
Release | : 1975 |
Genre | : Localization theory |
ISBN | : |
Author | : Andrew Ranicki |
Publisher | : Cambridge University Press |
Total Pages | : 332 |
Release | : 2006-02-09 |
Genre | : Mathematics |
ISBN | : 9780521681605 |
Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.
Author | : Daniel Wood Krider |
Publisher | : |
Total Pages | : 75 |
Release | : 1970 |
Genre | : Rings (Algebra) |
ISBN | : |
Author | : K. R. Goodearl |
Publisher | : Cambridge University Press |
Total Pages | : 372 |
Release | : 2004-07-12 |
Genre | : 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 | : Surender K. Jain |
Publisher | : Springer |
Total Pages | : 173 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540467459 |
The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.
Author | : Surender K. Jain |
Publisher | : Springer |
Total Pages | : 168 |
Release | : 1990-10-24 |
Genre | : Mathematics |
ISBN | : 9783540531647 |
The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.
Author | : John C. McConnell |
Publisher | : American Mathematical Soc. |
Total Pages | : 658 |
Release | : 2001 |
Genre | : 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 | : Soon-Kiong Sim |
Publisher | : |
Total Pages | : 0 |
Release | : 1972 |
Genre | : Rings (Algebra) |
ISBN | : |
Author | : Matej Brešar |
Publisher | : Springer |
Total Pages | : 227 |
Release | : 2014-10-14 |
Genre | : Mathematics |
ISBN | : 3319086936 |
Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.