# Associated primes, integral closures and ideal topologies

Colloquium Mathematicae (2006)

- Volume: 105, Issue: 1, page 35-43
- ISSN: 0010-1354

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topReza Naghipour. "Associated primes, integral closures and ideal topologies." Colloquium Mathematicae 105.1 (2006): 35-43. <http://eudml.org/doc/286241>.

@article{RezaNaghipour2006,

abstract = {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 $A*_\{a\}(,N) := ⋃ _\{n≥1\} Ass_\{R\}R/(ⁿ)^\{(N)\}_\{a\}$ of associated primes is finite. The purpose of this paper is to show that the topology on N defined by $\{(ⁿ)_\{a\}^\{(N)\}:_\{R\} ⟨⟩\}_\{n≥1\}$ is finer than the topology defined by $\{(ⁿ)_\{a\}^\{(N)\}\}_\{n≥1\}$ 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 $A*_\{a\}(,N) = Q̅*(,N)$.},

author = {Reza Naghipour},

journal = {Colloquium Mathematicae},

keywords = {integral closure; quintasymptotic primes; asymptotic sequence},

language = {eng},

number = {1},

pages = {35-43},

title = {Associated primes, integral closures and ideal topologies},

url = {http://eudml.org/doc/286241},

volume = {105},

year = {2006},

}

TY - JOUR

AU - Reza Naghipour

TI - Associated primes, integral closures and ideal topologies

JO - Colloquium Mathematicae

PY - 2006

VL - 105

IS - 1

SP - 35

EP - 43

AB - 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 $A*_{a}(,N) := ⋃ _{n≥1} Ass_{R}R/(ⁿ)^{(N)}_{a}$ of associated primes is finite. The purpose of this paper is to show that the topology on N defined by ${(ⁿ)_{a}^{(N)}:_{R} ⟨⟩}_{n≥1}$ is finer than the topology defined by ${(ⁿ)_{a}^{(N)}}_{n≥1}$ 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 $A*_{a}(,N) = Q̅*(,N)$.

LA - eng

KW - integral closure; quintasymptotic primes; asymptotic sequence

UR - http://eudml.org/doc/286241

ER -

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