A generalization of semiregular and semiperfect modules


ALGEBRA COLLOQUIUM, vol.15, no.4, pp.667-680, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1142/s1005386708000631
  • Title of Journal : ALGEBRA COLLOQUIUM
  • Page Numbers: pp.667-680


Let U be a submodule of a module M. We call U a strongly lifting submodule of M if whenever M/U = (A+U) = U-circle plus(B+U) =U, then M = P circle plus Q such that P <= A, (A+U)=U = (P+U) = U and (B+U) = U = (Q+U) =U. This definition is a generalization of strongly lifting ideals defined by Nichols on and Zhou. In this paper, we investigate some properties of strongly lifting submodules and characterize U-semiregular and U-semiperfect modules by using strongly lifting submodules. Results are applied to characterize rings R satisfying that every(projective)leftR-module M is t(M)-semiperfect for some preradicals such as Rad, Z(2) and delta.