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Vietnam Journal of Mathematics 36:3(2008)
315-325
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On Prime and Weakly Prime Submodules
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A. Azizi
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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  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.
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2000 Mathematics Subject Classification: 13C99, 13C13,
13E05, 13F05, 13F15.
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Keywords: Prime submodule, radical equality, set of
zero divisors, weakly prime submodule.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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