【摘 要】
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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 M I > O.In this paper,
【机 构】
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Department of Mathematics,University of Tabriz,51664 Tabriz,Iran;Institute for Studies in Theoretica
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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 M I > O.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 Nof M,the sequences Ass R M/(InN)a and hssR(InM)a/(InN)a (n=1,2,...) of associated prime ideals are increasing and ultimately constant for large n.
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