AFRICA MATHEMATICS ANNALS

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 be an associative ring with and an unitary -module. is said to be a Dedekind finite module if is not isomorphic to any proper direct summand of itself. The ring 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.