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Paper IPM / M / 7820  


Abstract:  
Let \fraka ⊆ \frakb be ideals of a Noetherian ring
R, and let N be a nonzero finitely generated Rmodule. 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} Ass_{R}R/(\frakb^{n})^{(N)}_{a} of associated primes is finite. The
purpose of this paper is to show that the topology on N defined
by {(\fraka^{n})^{(N)}_{a}:_{R}〈\frakb〉}_{n ≥ 1} is finer than the
topology defined by
{(\frakb^{n})^{(N)}_{a}}_{n ≥ 1}if 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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