Annales Mathematiques Africaines


Aller au contenu

Article39

Contenu > Anciens Numéros > 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.


Abstract:

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.

Accueil | Comité de Rédaction | A propos du journal | Abonnement | Contenu | Plan du site


Revenir au contenu | Revenir au menu