On Commutative EKFN-ring with Ascending Chain Condition on Annihilators

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.