Invariance of Modules Under Automorphisms of Their Envelopes and Covers

Front matter
Copyright
Contents
Preface
1 Preliminaries
	1.1 Basics of Ring Theory and Module Theory
	1.2 Simple and Semisimple Modules
	1.3 Essential and Closed Submodules
	1.4 Prime Rings and Semiprime Rings
	1.5 Classical Rings of Fractions and Semiprime Goldie Rings
	1.6 Local, Semilocal and Semiperfect Rings
	1.7 Injective and Projective Modules
	1.8 Injective Envelope and Quasi-Injective Modules
	1.9 Flat Modules
	1.10 Exchange Property of Modules
	1.11 Pure-Injective and Cotorsion Modules
2 Modules Invariant under Antomorphisms of Envelopes
	2.1 Introduction to Envelopes
	2.2 Modules Invariant under Endomorphisms and Automorphisms
	2.3 Additive Unit Structure of von Neumann Regular Rings
	2.4 Applications of Additive Unit Structure of von Neumann Regular Rings
3 Structure and Properties of Modules Invariant under Automorphisms
	3.1 Structure of Modules Invariant under Automorphisms
	3.2 Properties of Modules Invariant under Automorphisms
	3.3 Applications
	3.4 Modules Invariant under Monomorphisms
4 Automorphism-Invariant Modules
	4.1 Some Characterizations of Automorphism-Invariant Modules
	4.2 Nonsingular Automorphism-lnvariant Rings
	4.3 When Is an Automorphism-Invariant Module a Quasi-Injective Module
	4.4 Rings Whose Cyclic Modules Are Automorphism-Invariant
	4.5 Rings Whose Each One-Sided Ideal Is Automorphism-Invariant
5 Modules Coinvariant under Automorphisms of their Covers
	5.1 Structure and Properties
	5.2 Automorphism-Coinvariant Modules
	5.3 Dual Automorphism-Invariant Modules
6 Schroder-Bernstein Problem
	6.1 Schroder-Bernstein Problem for X-Endomorphism Invariant Modules
	6.2 Schroder-Bernstein Problem for Automorphism-Invariant Modules
7 Automorphism-Extendable Modules
	7.1 General Properties of Automorphism-Extendable Modules
	7.2 Semi-Artinian Automorphism-Extendable Modules
	7.3 Automorphism-Extendable Modules that Are Not Singular
	7.4 Modules over Strongly Prime Rings
	7.5 Modules over Hereditary Prime Rings
	7.6 General Properties of Endomorphism-Extendable Modules and Rings
	7.7 Annihilators that Are Ideals
	7.8 Completely Integrally Closed Subrings and Self-Injective Rings
	7.9 Endomorphism-Liftable and π-Projective Modules
	7.10 Rings Whose Cyclic Modules are Endomorphism-Extendable
8 Automorpllism-Liftable Modules
	8.1 Automorphism-Liftable and Endomorphism-Liftable Modules
	8.2 Non-Primitive Hereditary Noetherian Prime Rings
	8.3 Non-Primitive Dedekind Prime Rings
	8.4 Idempotent-Lifted Modules and π-Projective Modules
9 Open Problems
References
Index