Weakly automorphism invariant modules and essential tightness


Kosan M. T. , Truong Cong Quynh T. C. Q. , Sahinkaya S.

COMMUNICATIONS IN ALGEBRA, vol.45, no.8, pp.3531-3541, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1238094
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.3531-3541

Abstract

While a module is pseudo-injective if and only if it is automorphism-invariant, it was not known whether automorphism-invariant modules are tight. It is shown that weakly automorphism-invariant modules are precisely essentially tight. We give various examples of weakly automorphism-invariant and essentially tight modules and study their properties. Some particular results: (1) R is a semiprime right and left Goldie ring if and only if every right (left) ideal is weakly injective if and only if every right (left) ideal is weakly automorphism invariant; (2) R is a CEP-ring if and only if R is right artinian and every indecomposable projective right R-module is uniform and essentially R-tight.