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Paper   IPM / M / 8290
School of Mathematics
  Title:   Asymptotic behavior of integral closures in modules
  Author(s):  R. Naghipour (Joint with P. Schenzel)
  Status:   Published
  Journal: Algebra Colloq.
  Vol.:  14
  Year:  2007
  Pages:   505 - 514
  Supported by:  IPM
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 NNa 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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