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Contents > Past issues > Volume 4

A Characterisation of Commutative Rings in Which every Dedekind
Finite Module is Finitely Cogenerated

Sidy Demba TOURÉ, Ibrahima LABOU,
et Mamadou SANGHARÉ

Département de Mathematiques et Informatique,
Faculté des Sciences et Techniques,
Université Cheikh Anta Diop de Dakar, Sénégal

Mathematics Subject Classification: [2010] :
Keywords: Dedekind finite module, hopfian module, Co-hopfian module, artinian principal ideal ring, SCDF-ring, SCI-ring, SCS-ring.


Let $R$ be an associative ring with $1\neq 0$ and $M$ an unitary $R$-module. $M $ is said to be a Dedekind finite module if $M$ is not isomorphic to any proper direct summand of itself. The ring $R$ is called SCDF - ring if every Dedekind finite module is finitely cogenerated. In this note we will prove that artinian principal ideal commutative rings characterize commutative SCDF-rings.

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