IJPAM: Volume 86, No. 5 (2013)

ON COMMUTATIVE EKFN-RING WITH ASCENDING
CHAIN CONDITION ON ANNIHILATORS

Mohameth Alassane Ndiaye1, Cheikh Thiécoumba Gueye2
1,2Laboratoire 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


Abstract. We consider the class E of endo-noetherian modules, ie the modules M satisfying the ascending chain condition for endomorphic kernels: the chain Ker f1 ⊂ Ker f2 ⊂ ... ⊂ Ker fn ⊂ ... is stationary, where fn ∈ End(M). And let N be the class of noetherian modules. It is well known that every noetherian R-module M is endo-noetherian, but the converse is not true, so N ⊂ E. The aim of this work, is to characterize commutative rings for which E and N are identical.

Received: May 20, 2013

AMS Subject Classification: 13-XX

Key Words and Phrases: annihilator, Artinian, EKFN-ring, endo-noetherian, Hopfian, Noetherian, strongly Hopfian

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DOI: 10.12732/ijpam.v86i5.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 5