Rings whose CS modules are countably Sigma-CS

ER N. F.

COMMUNICATIONS IN ALGEBRA, vol.31, no.11, pp.5513-5523, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 11
  • Publication Date: 2003
  • Doi Number: 10.1081/agb-120023971
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5513-5523
  • Keywords: CS module, quasi-injective, continuous
  • Dokuz Eylül University Affiliated: No

Abstract

A module M is called a CS module if every submodule of M is essential in a direct summand of M. In this paper, among other results, we prove that for a ring R with finitely generated right socle the following are equivalent: i) For every CS right R-module M, M-(N) is CS; ii) R is a right artinian ring with all uniforms Sigma-quasi-injective.