On Commutative EKFN-ring with Ascending Chain Condition on Annihilators
Mohameth Alassane Ndiaye, Cheikh Thiecoumba Gueye
Journal of Advances in Mathematics and Computer Science · pp. 426–431 · Published 13 Nov 2013
10.9734/BJMCS/2014/5567Abstract
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.
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