ON ADS MODULES AND RINGS


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

COMMUNICATIONS IN ALGEBRA, vol.42, no.8, pp.3541-3551, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 8
  • Publication Date: 2014
  • Doi Number: 10.1080/00927872.2013.788185
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.3541-3551

Abstract

A right module M over a ring R is said to be ADS if for every decomposition M=S circle plus T and every complement T of S, we have M=S circle plus T. In this article, we study and provide several new characterizations of this new class of modules. We prove that M is semisimple if and only if every module in sigma[M] is ADS. SC and SI rings also characterized by the ADS notion. A ring R is right SC-ring if and only if every 2-generated singular R-module is ADS.