On Perfect Commutative EIFA-rings
Mohameth Alassane Ndiaye *
Laboratoire d’Algèbre, de Cryptographie, de Géométrie Algébrique et Applications (LACGAA), Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, BP 5005 Dakar, Sénégal.
Cheikh Thiécoumba Gueye
Laboratoire d’Algèbre, de Cryptographie, de Géométrie Algébrique et Applications (LACGAA), Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, BP 5005 Dakar, Sénégal.
*Author to whom correspondence should be addressed.
Abstract
We consider the class F of endo-Artinian modules, i.e. the modules M which satisfying the descending chain condition for endomorphic images: any descending chain 
is stationary, where 
. Let A be the class of Artinian modules. It is clear that every Artinian R-moduleM is endo-Artinian, so A ⊂ F, but the converse is not true. Indeed, 
is a non-Artinian 
-module which is endo-Artinian. The aim of this work, is to characterize perfect commutative rings for which F and A are identical.
Keywords: Artinian, EIFA-ring, endo-Artinian, perfect