Invariance of Modules Under Automorphisms of Their Envelopes and Covers PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Invariance of Modules Under Automorphisms of Their Envelopes and Covers PDF full book. Access full book title Invariance of Modules Under Automorphisms of Their Envelopes and Covers by Ashish K. Srivastava. Download full books in PDF and EPUB format.
Author: Ashish K. Srivastava
Publisher:
ISBN:
Category :
Languages : en
Pages : 223
Get Book Here
Book Description
"The study of modules which are invariant under the action of certain subsets of the endomorphism ring of their injective envelope can be drawn back to the pioneering work of Johnson and Wong in which they characterized quasi-injective modules as those modules which are invariant under any endomorphism of their injective envelope. Later, Dickson and Fuller studied modules which are invariant under the group of all automorphisms of their injective envelope and proved that any indecomposable automorphism-invariant module over an F-algebra A is quasi-injective provided that F is a field with more than two elements. But after that this topic remained in dormant stage for some time until Lee and Zhou picked it up again in their paper where they called such modules auto-invariant modules. But the major breakthrough on this topic came from two papers that appeared a few months later: one of them was a paper of Er, Singh and Srivastava where they proved that the automorphism-invariant modul
Author: Ashish K. Srivastava
Publisher:
ISBN:
Category :
Languages : en
Pages : 223
Get Book Here
Book Description
"The study of modules which are invariant under the action of certain subsets of the endomorphism ring of their injective envelope can be drawn back to the pioneering work of Johnson and Wong in which they characterized quasi-injective modules as those modules which are invariant under any endomorphism of their injective envelope. Later, Dickson and Fuller studied modules which are invariant under the group of all automorphisms of their injective envelope and proved that any indecomposable automorphism-invariant module over an F-algebra A is quasi-injective provided that F is a field with more than two elements. But after that this topic remained in dormant stage for some time until Lee and Zhou picked it up again in their paper where they called such modules auto-invariant modules. But the major breakthrough on this topic came from two papers that appeared a few months later: one of them was a paper of Er, Singh and Srivastava where they proved that the automorphism-invariant modul
Author: Ashish K. Srivastava
Publisher: Cambridge University Press
ISBN: 1108960162
Category : Mathematics
Languages : en
Pages : 235
Get Book Here
Book Description
The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
Author: J.R. Garcia Rozas
Publisher: CRC Press
ISBN: 9781584880042
Category : Mathematics
Languages : en
Pages : 160
Get Book Here
Book Description
Over the last few years, the study of complexes has become increasingly important. To date, however, most of the research is scattered throughout the literature or available only as lecture notes. Covers and Envelopes in the Category of Complexes of Modules collects these scattered notes and results into a single, concise volume that provides an account of recent developments in the theory and presents several new and important ideas. The author introduces the theory of complexes of modules using only elementary tools-making the field more accessible to non-specialists. He focuses the study on envelopes and covers in this category with respect to some well established and important classes of complexes. He places particular emphasis on DG-injective and DG-projective complexes and flat and DG-flat covers. Other topics covered include Zorn's Lemma for categories, preserving and reflecting covers by functors, orthogonality in the category of complexes, Gorenstein injective and projective complexes, and pure sequences of complexes. Along with its value as a collection of recent work in the field, Covers and Envelopes in the Category of Complexes of Modules presents powerful new ideas that will undoubtedly advance homological methods. Mathematicians-especially researchers in module theory and homological algebra-will welcome this volume as a reference guide and for its new and important results.
Author: Ashish K. Srivastava
Publisher: Cambridge University Press
ISBN: 1108949533
Category : Mathematics
Languages : en
Pages : 235
Get Book Here
Book Description
Provides a unified treatment of the study of modules invariant under automorphisms of their envelopes and covers.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 974
Get Book Here
Book Description
Author: Elias G. Katsoulis
Publisher: American Mathematical Soc.
ISBN: 1470435454
Category : C*-algebras
Languages : en
Pages : 85
Get Book Here
Book Description
The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
Author: Pierre Simon
Publisher: Cambridge University Press
ISBN: 1107057752
Category : Mathematics
Languages : en
Pages : 165
Get Book Here
Book Description
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Author: Kevin Costello
Publisher: Cambridge University Press
ISBN: 1107163102
Category : Mathematics
Languages : en
Pages : 399
Get Book Here
Book Description
This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.
Author: S. Chmutov
Publisher: Cambridge University Press
ISBN: 1107020832
Category : Mathematics
Languages : en
Pages : 521
Get Book Here
Book Description
A detailed exposition of the theory with an emphasis on its combinatorial aspects.
