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Semi M-Projective and Semi N-Injective Modules
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  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 1,  2016, pp.83-94
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.1.83
 Title & Authors
Semi M-Projective and Semi N-Injective Modules
Hakmi, Hamza;
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 Abstract
Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and for all , if and only if a module M is semi N-injective and for all . Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any there exists such that , if and only if a module M is direct N-injective and for any there exists such that . The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.
 Keywords
Regular ring;Semi-potent ring;Radical Jacobson;Semi M-injective (N-projective) modules;direct M-injective (N-projective) modules;Endomorphism ring;
 Language
English
 Cited by
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