“School of Mathematics”
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| Paper IPM / M / 8290 |
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| Abstract: | |
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Let R be a commutative Noetherian Nagata ring, let M be a
non-zero finitely generated R-module, and let I be an ideal of
R such that height MI > 0. In this paper, there is a
definition of the integral closure Na for any submodule N
of M extending Rees' definition for the case of a domain. As the
main results, it is shown that the operation N→ Na
on the set of submodules N of M is a semi-prime operation, and
for any submodule N of M, the sequences AssRM/(InN)a and AssR(In M)a/(In N)a(n = 1,2, ... ) of
associated prime ideals are increasing and ultimately constant for
large n.
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