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Information Journal Paper

Title

APPLICATIONS OF EPI-RETRACTABLE AND CO-EPI-RETRACTABLE MODULES

Author(s)

 MOSTAFANASAB H.

Pages

  903-917

Abstract

 A module M is called EPI-RETRACTABLE if every submodule of M is a homomorphic image of M. Dually, a module M is called co-EPI-RETRACTABLE if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (respectively, copri) if RR (respectively, RR) is co-EPI-RETRACTABLE. It is proved that if R is a left principal right duo ring, then every left ideal of R is an EPI-RETRACTABLE R-module. A co-pli strongly prime ring R is a simple ring. A left self-injective co-pli ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a pli ring if and only if it is a co-pri ring. Moreover, if R is a left perfect ring such that every projective R-module is co-EPI-RETRACTABLE, then R is a quasi-Frobenius ring.

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