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Endomorphism Rings Of Quasi-Projective Modules
And Quasi-Injective Modules



Sidy Demba TOURÉ, Ibrahima LABOU,
Sidi Mohamed OULD MOHAMED
and Mamadou SANGHARÉ
Département de Mathématiques et Informatique
Faculté des Sciences et Techniques
de l'Université Cheikh Anta Diop de Dakar, Sénégal



Mathematics Subject Classification: [2010] : 58C06, 58C07, 58C35, 49Q20
Keywords: quasi - projective module, quasi-injective module, hopfian module, Co-Hopfian module, generalized hopfian module, weakly Hopfian module, Dedekind finite module



Abstract:

Let $R$ be an associative ring with $1\neq 0$ and $M$ an unitary left $R$-module. $M$ is said to be Hopfian (resp. Co-hopfian) if every surjective (resp. injective) endomorphism of $M$ is an automorphism. $M $ is said to be generalized hopfian (resp. Weakly Co-hopfian) if every surjective (resp. injective) endomorphism of $M$ is superfluous (resp. essential). $M$ is said to be Dedekind finite module if $M$ is not isomorphic to any proper direct summand of itself. The purpose of this note is to prove some results relatively to quasi-projective modules and quasi-injective modules.

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