Weakly Associated Prime Filtration |
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Authors: | S Yassemi |
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Institution: | (1) Department of Mathematics, University of Tehran, P.O. Box, 13145-448 Tehran, Iran |
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Abstract: | Let R be a (not necessarily Noetherian) commutative ring and let M be a (not necessarily finitely generated) R-module. We characterize the modules with only finitely many weakly associated primes as those modules M admitting a chain 0 = M
0 M
1 ... M
n
= M of submodules together with prime ideals p1, p2,...,p
n
such that the set of weakly associated primes of M
i
/M
i-1 is equal to {p
i
} for all 1 i n. Let M = gra(M) =
n 0a
n
M/a
n+1
M be the corresponding graded module over the graded ring R = gra(R) =
n 0a
n
/a
n+1. It is shown that the union of the set of weakly associated primes of..... |
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Keywords: | Weakly associated prime filtration |
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