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In Helm and Miller (2003, Section 8), the authors posed the problem of which
faces of a saturated affine semigroup $Q$ correspond to prime
ideals associated to the local cohomology module
$H^{i}_{I}(\omega_{R})$ where $\omega_{R}$ is the canonical module
of the semigroup ring $R = k[Q]$, $k$ a field, and $I$ is a
monomial ideal in $R$. In this paper we will give a solution in
the case that $Q$ is simplicial. We will also consider a similar
problem for attached primes of the local cohomology module
$H^{i}_{m}(M)$ where $M$ is a squarefree module (in sense of
Definition 2.7) and $m$ is the homogeneous maximal ideal of $R$. As
a result, we will show that for a squarefree monomial ideal $I$ in
a normal simplicial semigroup ring $R$ and each integer $i\geq 0$,
we have Ass $H^{i}_{I}(\omega_{R})$ = Att $H^{d-i}_{m}(R/ I)$
where $d$= dim $R$.
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