  The Hartshorne-Speiser-Lyubeznik number is a numerical invariant that can
often be used to bound the Frobenius test exponent of positive characteristic
rings. In this paper we look at positive characteristic semigroup rings
generated by affine torsion-free abelian cancellative pointed semigroups that
contain an identity, and compute an upper bound for the
Hartshorne-Speiser-Lyubeznik number of their top local cohomology module at the
maximal monomial ideal.
