Group rings and semigroup rings over strong Mori domains, II

Let R be an integral domain and let S be a torsion-free cancellative additive monoid with quotient group G. We show that the semigroup ring R[X;S] is a strong Mori domain if and only if R is a strong Mori domain, S is a strong Mori semigroup, and each nonzero element of G is of type (0,0,0,…).