On normal affine semigroups (Q1301279)

Let \(S\) be an affine semigroup, i.e., a finitely generated additive submonoid of \(\mathbb{N}^k\). Then \(S\) is said to be normal if \(ng\in S\) implies \(g\in S\), where \(n\geq 1\) is an integer and \(g\in G(S)\), the group generated by \(S\). In this paper, the authors develop algorithms to (1) check, from the generators of an affine semigroup, whether the semigroup is normal, and (2) determine, from a finite presentation of a semigroup, whether the semigroup is affine and normal. Applications are also given for computing the nonnegative integer solutions to a system of linear equations with rational coefficients, determining whether a semigroup ring is Gorenstein, and computing the dual of a semigroup.