A generalization of semiregular and semiperfect modules


ÖZCAN A. Ç. , AYDOĞDU P.

ALGEBRA COLLOQUIUM, cilt.15, ss.667-680, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 15 Konu: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1142/s1005386708000631
  • Dergi Adı: ALGEBRA COLLOQUIUM
  • Sayfa Sayıları: ss.667-680

Özet

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.