
Vietnam Journal of Mathematics 36:3(2008)
315325

On Prime and Weakly Prime Submodules

A. Azizi

Abstract. A proper submodule N of an Rmodule M is called
a weakly prime [resp. a prime] submodule, if for any elements a, b R
and x M,
the condition abx N
[resp. ax N]
implies that ax N
or bx N
[resp. x N
or aM 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 equality, set of
zero divisors, weakly prime submodule.


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by Vietnam Academy of Science and Technology & Vietnam Mathematical
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Published
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