A generalization of projective covers

ALKAN M., Nicholson W. K., ÖZCAN A. Ç.

JOURNAL OF ALGEBRA, vol.319, no.12, pp.4947-4960, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 319 Issue: 12
  • Publication Date: 2008
  • Doi Number: 10.1016/j.jalgebra.2008.03.029
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4947-4960
  • Hacettepe University Affiliated: Yes

Abstract

Let M be a left module over a ring R and I an ideal of R. We call (P, f) a projective I-cover of M if f is an epimorphism from P to M, P is projective, Ker f subset of I P, and whenever P = Ker f + X, then there exists a summand Y of P in Ker f such that P = Y + X. This definition generalizes projective covers and projective delta-covers. Similar to semiregular and serniperfect rings, we characterize I-semiregular and I-semiperfect rings which are defined by Yousif and Zhou using projective I-covers. In particular, we consider certain ideals such as Z((R) R), Soc((R) R), delta(R R) and Z(2) ((R) R). (c) 2008 Elsevier Inc. All rights reserved.