ON GENERALIZATIONS OF SEMIPERFECT AND PERFECT RINGS


DEMİRCİ Y. M.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.42, no.6, pp.1441-1450, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 6
  • Publication Date: 2016
  • Title of Journal : BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1441-1450
  • Keywords: Flat cover, flat B-cover, flat strong cover, G-semiperfect ring, perfect ring, FLAT COVERS, MODULES

Abstract

We call a ring R right generalized semiperfect if every simple right R-module is an epimorphic image of a flat right R-module with small kernel, that is, every simple right R-module has a flat B-cover. We give some properties of such rings along with examples. We introduce flat strong covers as flat covers which are also flat B-covers and give characterizations of A-perfect, B-perfect and perfect rings in terms of flat strong covers.