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 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.
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.