MODULES WHICH ARE INVARIANT UNDER AUTOMORPHISMS OF THEIR INJECTIVE HULLS-Reference-Cited by-同舟云学术

MODULES WHICH ARE INVARIANT UNDER AUTOMORPHISMS OF THEIR INJECTIVE HULLS

Published:2012-12-16 Issue:02 Volume:12 Page:1250159
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

LEE TSIU-KWEN¹,ZHOU YIQIANG²

Affiliation:

1. Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Nl A1C 5S7, Canada

Abstract

A module is defined to be an automorphism-invariant module if it is invariant under automorphisms of its injective hull. Quasi-injective modules and, more generally, pseudo-injective modules are all automorphism-invariant. Here we develop basic properties of these modules, and discuss when an automorphism-invariant module is quasi-injective or injective. Some known results on quasi-injective and pseudo-injective modules are extended.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498812501599

Reference22 articles.

1. Modules which are invariant under monomorphisms of their injective hulls

2. Rings over which certain modules are injective

3. Continuous modules are clean

4. Exchange rings, units and idempotents

5. Classes of Modules

Cited by 79 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On semiperfect a -rings;Ukrains’kyi Matematychnyi Zhurnal;2024-07-03

2. On Nilpotent-invariant One-sided Ideals;Acta Mathematica Vietnamica;2024-03

3. Endomorphism rings and formal matrix rings of pseudo-projective modules;FILOMAT;2024

4. Algebraic Structures on Smooth Vector Fields;Symmetry;2023-12-03

5. On Annihilators and Quasi-Frobenius Rings;Lobachevskii Journal of Mathematics;2023-12