International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 53-56, Pages 2911-2913
doi:10.1155/S0161171204311282
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
Abstract
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.