F-Rational Rings and the Integral Closures of Ideals II

2019 ◽  
pp. 1-12
Author(s):  
Ian M. Aberbach ◽  
Craig Huneke
Keyword(s):  
Integral Closures

scholarly journals Computing Local Integral Closures

2001 ◽  
Vol 32 (3) ◽  
pp. 211-230 ◽  
Author(s):  
Emmanuel Hallouin
Keyword(s):  
Local Integral ◽  
Integral Closures

Asymptotic Behavior of Integral Closures in Modules

2007 ◽  
Vol 14 (03) ◽  
pp. 505-514 ◽  
Author(s):  
R. Naghipour ◽  
P. Schenzel
Keyword(s):  
Asymptotic Behavior ◽  
Integral Closure ◽  
Prime Ideals ◽  
Finitely Generated ◽  
Large N ◽  
Nagata Ring ◽  
Associated Prime Ideals ◽  
Integral Closures ◽  
Definition Of ◽  
Associated Prime

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.

ON THE INTEGRAL CLOSURES OF IDEALS

2007 ◽  
Vol 29 (4) ◽  
pp. 653-666 ◽  
Author(s):  
H. Ansari-Toroghy ◽  
F. Dorostkar
Keyword(s):  
Integral Closures
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