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Asymptotic Behavior of Integral Closures in Modules.
- Source :
-
Algebra Colloquium . Sep2007, Vol. 14 Issue 3, p505-514. 10p. - Publication Year :
- 2007
-
Abstract
- 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 heightMI > 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 AssR M/(InN)a and AssR (InM)a/(InN)a(n=1,2,...) of associated prime ideals are increasing and ultimately constant for large n. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10053867
- Volume :
- 14
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Algebra Colloquium
- Publication Type :
- Academic Journal
- Accession number :
- 25602559
- Full Text :
- https://doi.org/10.1142/S1005386707000466