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Let $I$ be an ideal of a Noetherian ring $R$, $N$ a finitely
generated $R$-module and let $S$ be a multiplicatively closed
subset of $R$. We define the $n$-the $(S)$-symbolic power of
$I$ w.r.t. $N$ as $S(I^nN)=\cup_{s\in S}(I^n N:_N s)$. The
purpose of this paper is to show that the topologies defined by
$\{I^n N\}_{n\geq 0}$ are equivalent (resp. linearly equivalent) if
and only if $S$ is disjoint from the quintessential (resp. essential)
primes of $I$ w.r.t. $N$.
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