Simple-direct-modules


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

COMMUNICATIONS IN ALGEBRA, vol.45, no.8, pp.3643-3652, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1243697
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.3643-3652
  • Keywords: Artinian serial rings and uniserial rings, C3-and D3-modules, CS and lifting modules, simple-direct-injective and simple-direct-projective modules, SSP and SIP modules, INJECTIVE-MODULES, RINGS

Abstract

A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with AB, and (BM)-M-circle plus, then A(circle plus)M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M/AB(circle plus)M and B simple, then A(circle plus)M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J(2)(R)=0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module).