International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 54, Pages 2911-2913

Two versions of Nakayama lemma for multiplication modules

Reza Ameri

Department of Mathematics and Statistics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47415, Iran

Received 24 November 2003

Copyright © 2004 Reza Ameri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this note is to generalize the Nakayama lemma to a class of multiplication modules over commutative rings with identity. In this note, by considering the notion of multiplication modules and the product of submodules of them, we state and prove two versions of Nakayama lemma for such modules. In the first version we give some equivalent conditions for faithful finitely generated multiplication modules, and in the second version we give them for faithful multiplication modules with a minimal generating set.