Simple-Direct-Projective Modules


Ibrahim Y., Kosan M. T. , Truong Cong Quynh T. C. Q. , Yousif M.

COMMUNICATIONS IN ALGEBRA, vol.44, no.12, pp.5163-5178, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 12
  • Publication Date: 2016
  • Doi Number: 10.1080/00927872.2016.1147574
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.5163-5178

Abstract

In this paper, we introduce and study the dual notion of simple-direct-injective modules. Namely, a right R-module M is called simple-direct-projective if, whenever A and B are submodules of M with B simple and M/AB(circle plus)M, then A(circle plus)M. Several characterizations of simple-direct-projective modules are provided and used to describe some well-known classes of rings. For example, it is shown that a ring R is artinian and serial with J(2)(R)=0 if and only if every simple-direct-projective right R-module is quasi-projective if and only if every simple-direct-projective right R -module is a D3-module. It is also shown that a ring R is uniserial with J(2)(R)=0 if and only if every simple-direct-projective right R-module is a C3-module if and only if every simple-direct-injective right R -module is a D3-module.