Asymptotic Behavior of Integral Closures in Modules
Keyword(s):
Large N
◽
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 Ass R M/(InN)a and Ass R (InM)a/(InN)a(n=1,2,…) of associated prime ideals are increasing and ultimately constant for large n.
Keyword(s):
2016 ◽
Vol 36
(1)
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pp. 15
Keyword(s):
2010 ◽
Vol 38
(12)
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pp. 4416-4429
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2004 ◽
Vol 03
(02)
◽
pp. 193-205
◽