On Commutative EKFN-ring with Ascending Chain Condition on Annihilators
Mohameth Alassane Ndiaye *
Laboratoire d’Algebre, de Cryptographie, de Geometrie Algebrique et Applications (LACGAA), Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, Universite Cheikh Anta Diop, BP 5005 Dakar, Senegal.
Cheikh Thiecoumba Gueye
Laboratoire d’Algebre, de Cryptographie, de Geometrie Algebrique et Applications (LACGAA), Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, Universite Cheikh Anta Diop, BP 5005 Dakar, Senegal.
*Author to whom correspondence should be addressed.
Abstract
We consider the class E of endo-Noetherian modules, i.e. the modules M which satisfying the
ascending chain condition for endomorphic kernels: any ascending chain Kerf1 Kerf2
Kerfn is stationary, where fi 2 End(M). Let N be the class of Noetherian modules. It is
clear that every Noetherian R-module M is endo-Noetherian, so N E, but the converse is not
true. Indeed, Q is a non-Noetherian Z-module which is endo-Noetherian. The aim of this work, is
to characterize commutative rings for which E and N are identical.
Keywords: Annihilator, Artinian, EKFN-ring, endo-Noetherian, hopfian, Noetherian, strongly hopfian.