Associated primes, integral closures and ideal topologies

• Autorzy: Reza Naghipour
• Języki publikacji: 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 $A*_{a}(𝔞,N) = Q̅*(𝔞,N)$.

Kategorie tematyczne

• 13J30: Real algebra
• 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 105
• Numer: 1
• Strony: 35-43

Daty

wydano

2006

Twórcy

autor

Reza Naghipour

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

Identyfikatory

DOI

10.4064/cm105-1-4