Korean J. Math. Vol. 25 No. 4 (2017) pp.587-606
DOI: https://doi.org/10.11568/kjm.2017.25.4.587

(Co) retractability and (Co) Semi-potency

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Hamza Ibrahim Hakmi


This paper is a continuation of study semi-potentness endomorphism rings of module. We give some other characterizations of endomorphism ring to be semi-potent. New results are obtained including necessary and sufficient conditions for the endomorphism ring of semi(injective) projective module to be semi-potent. Finally, we characterize a module $M$ whose endomorphism ring it is semi-potent via direct(injective) projective modules. Several properties of the endomorphism ring of a semi(injective) projective module are obtained. Besides to that, many necessary and sufficient conditions are obtained for semi-projective, semi-injective modules to be semi-potent and co-semi-potent modules.

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