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| Paper IPM / M / 7820 |
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| Abstract: | |
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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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