Associated primes, integral closures and ideal topologies

Reza Naghipour

Reza Naghipour

Colloquium Mathematicae, Tome 106 (2006), p. 35-43 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ⊆ be ideals of a Noetherian ring R, and let N be a non-zero finitely generated R-module. The set Q̅*(,N) of quintasymptotic primes of with respect to N was originally introduced by McAdam. Also, it has been shown by Naghipour and Schenzel that the set $A *_{a} (, N) : = ⋃_{n \geq 1} A s s_{R} R / {(ⁿ)}_{a}^{(N)}$ of associated primes is finite. The purpose of this paper is to show that the topology on N defined by ${{(ⁿ)}_{a}^{(N)} :_{R} ⟨ ⟩}_{n \geq 1}$ is finer than the topology defined by ${(ⁿ)}_{a}^{(N)}_{n \geq 1}$ if and only if $A *_{a} (, N)$ is disjoint from the quintasymptotic primes of with respect to N. Moreover, we show that if is generated by an asymptotic sequence on N, then $A *_{a} (, N) = Q ̅ * (, N)$ .

Publié le : 2006-01-01

Zbl 1094.13010

EUDML-ID : urn:eudml:doc:286241

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     title = {Associated primes, integral closures and ideal topologies},
     journal = {Colloquium Mathematicae},
     volume = {106},
     year = {2006},
     pages = {35-43},
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Reza Naghipour. Associated primes, integral closures and ideal topologies. Colloquium Mathematicae, Tome 106 (2006) pp. 35-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-4/