Invariance Of Modules Under Automorphisms Of Their Envelopes And Covers
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Invariance of Modules under Automorphisms of their Envelopes and Covers
Author: Ashish K. Srivastava
language: en
Publisher: Cambridge University Press
Release Date: 2021-03-18
Provides a unified treatment of the study of modules invariant under automorphisms of their envelopes and covers.
Invariance of Modules Under Automorphisms of Their Envelopes and Covers
"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
Advances in Rings and Modules
Author: Sergio R. López-Permouth
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-09-06
This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.