Recent Issues Volume 37 1 2 3 4 Volume 36 1 2 3 4 Volume 35 1 2 3 4 Volume 34 1 2 3 4 Volume 33 1 2 3 4 Past Issues The Journal Cover Aims and Scope Subscription Information Editorial Board Instructions for Author Contact Us Related Links

Vietnam Journal of Mathematics 36:3(2008) 315-325  On Prime and Weakly Prime Submodules A. Azizi Abstract.  A proper submodule $N$ of an $R$-module $M$ is called a weakly prime [resp. a prime] submodule, if for any elements $a, b\in R$ and $x\in M,$ the condition $abx \in N$ [resp. $ax \in N$] implies that $ax\in N$ or $bx\in N$ [resp. $x\in N$ or $aM\subseteq N$]. In this paper the relations between weakly prime submodules of a module $M$ and weakly prime submodules of the localization of $M$ are studied. Some applications of these relations are given. Furthermore, the relations between the intersection of prime submodules and the intersection of weakly prime submodules are discussed.   2000 Mathematics Subject Classification: 13C99, 13C13, 13E05, 13F05, 13F15. Keywords: Prime submodule, radical equatlity, set of zero divisors, weakly prime submodule.

Vietnam Academy of Science and Technology & Vietnamese Mathematical Society © Copyright 2009 Vietnam Journal of Mathematics. All rights reserved.