Theoretical Mathematics & Applications

Endomorphism Rings of Essentially Pseudo Injective Modules

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  • Abstract

    In this paper some of the results on the endomorphism rings of essentially pseudo injective modules have been obtained. In particular, it is proved that for a uniform essentially pseudo injective module M, the socle of M is essential in M iff Jacobson radical of endomorphism ring of M is equal to the set of all homomorphisms from socle of M to M. It has been shown that the endomorphism ring of an essentially pseudo injective uniform module is local and the mono-endomorphism of an essentially pseudo injective uniform module is an automorphism. Finally, we found a characterization for a uniform module M to be essentially pseudo injective in terms of its injective hull.