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.
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.