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• # Artykuł - szczegóły

## Colloquium Mathematicum

2006 | 105 | 1 | 35-43

## Associated primes, integral closures and ideal topologies

EN

### Abstrakty

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

35-43

wydano
2006

### Twórcy

autor
• Department of Mathematics, University of Tabriz, Tabriz, Iran
• Institute for Studies, in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran