CSSES-MODULES and CSSES-RINGS


Leghwel A., Harmanci A.

GAZI UNIVERSITY JOURNAL OF SCIENCE, vol.18, no.3, pp.381-390, 2005 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 3
  • Publication Date: 2005
  • Title of Journal : GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Page Numbers: pp.381-390

Abstract

We study the structure of semiperfect, CS-Modules with essential socle. We call the module M CSSES-module if M is semiperfect, CS-module with essential socle. We will call the ring R right CSSES-ring if the right R-module R-R is CSSES-module. In this note among others we prove that [i] If R is right CF and left GIN-ring, then R is QF-ring if and only if R is right CS-ring if and only R is CSSES-ring. [ii] Every left Kasch right CF-ring is right CSSES-ring. [iii] If R is left Kasch and right IN-ring with equal left and right socles, then R is CSSES-ring.