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Paper   IPM / M / 7820
School of Mathematics
  Title:   Associated primes, integral closures and ideal topologies
  Author(s):  R. Naghipour
  Status:   Published
  Journal: Colloq. Math.
  Vol.:  105
  Year:  2006
  Pages:   35-43
  Supported by:  IPM
Let \fraka ⊆ \frakb be ideals of a Noetherian ring R, and let N be a non-zero finitely generated R-module. The set Q* (\fraka, N) of quintasymptotic primes of \fraka with respect to N was originally introduced by McAdam. Also, it has been shown by Naghipour and Schenzel that the set A*a(\frakb, N) : = ∪n ≥ 1 AssRR/(\frakbn)(N)a of associated primes is finite. The purpose of this paper is to show that the topology on N defined by {(\frakan)(N)a:R〈\frakb〉}n ≥ 1 is finer than the topology defined by {(\frakbn)(N)a}n ≥ 1if and only if A*a(\frakb, N) is disjoint from the quintasymptctic primes of \fraka with respect to N. Moreover, we show that if \fraka is generated by an asymptotic sequence on N, then A*a(\fraka, N) = Q* (\fraka, N)) .

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