RINGS WITH VARIATIONS OF FLAT COVERS


DEMİRCİ Y. M. , Turkmen E.

HONAM MATHEMATICAL JOURNAL, vol.41, no.4, pp.799-812, 2019 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.5831/hmj.2019.41.4.799
  • Title of Journal : HONAM MATHEMATICAL JOURNAL
  • Page Numbers: pp.799-812
  • Keywords: flat e-cover, e-perfect ring, flat-locally projective cover, perfect ring, PERFECT, SEMIPERFECT, MODULES, SUBMODULES

Abstract

We introduce flat e-covers of modules and define e-perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if flat covers of any R-module are projective covers, we study on the rings over which flat covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.