On delta-semiperfect modules


Hau Xuan Nguyen H. X. N. , Kosan M. T. , Zhou Y.

COMMUNICATIONS IN ALGEBRA, vol.46, no.11, pp.4965-4977, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 11
  • Publication Date: 2018
  • Doi Number: 10.1080/00927872.2018.1459650
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.4965-4977

Abstract

A submodule N of a module M is -small in M if N+XM for any proper submodule X of M with M/X singular. A projective -cover of a module M is a projective module P with an epimorphism to M whose kernel is -small in P. A module M is called -semiperfect if every factor module of M has a projective -cover. In this paper, we prove various properties, including a structure theorem and several characterizations, for -semiperfect modules. Our proofs can be adapted to generalize several results of Mares [8] and Nicholson [11] from projective semiperfect modules to arbitrary semiperfect modules.