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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1715-1724

On the prime submodules of multiplication modules

Mathematics Department, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran

Received 28 February 2002

Copyright © 2003 Hindawi Publishing Corporation. 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.


By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results.