On generalizations of semiperfect and perfect rings

Document Type: Research Paper

Author

Department of Mathematics, Sinop University, 57000, Sinop, Turkey.

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.

Keywords

Main Subjects


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Volume 42, Issue 6
November and December 2016
Pages 1441-1450
  • Receive Date: 02 July 2015
  • Revise Date: 08 September 2015
  • Accept Date: 15 September 2015