Semiperfect modules with respect to a preradical


Ozcan A. Ç. , ALKAN M.

COMMUNICATIONS IN ALGEBRA, vol.34, no.3, pp.841-856, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 3
  • Publication Date: 2006
  • Doi Number: 10.1080/00927870500441593
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.841-856

Abstract

In this article, we consider the module theoretic version of I-semiperfect rings R for an ideal I which are defined by Yousif and Zhou (2002). Let M be a left module over a ring R , N is an element of sigma[M], and tau(M) a preradical on sigma[M]. We call N tau(M)-semiperfect in sigma[M] if for any submodule K of N , there exists a decomposition K = A circle plus B such that A is a projective summand of N in sigma[M] and B <= tau(M) (N). We investigate conditions equivalent to being a tau(M)-semiperfect module, focusing on certain preradicals such as Z(M) , Soc , and delta(M) . Results are applied to characterize Noetherian QF-modules (with Rad (M) <= Soc(M)) and semisimple modules. Among others, we prove that if every R-module M is Soc-semiperfect, then R is a Harada and a co-Harada ring.