On the prime spectrum of commutative semigroup rings

Let A be an integral domain and S a torsion-free cancellative Abelian semigroup. By analogy with known results oil polynomial rings and group rings, results are sought for a number of properties of the semigroup ring A[S]. The properties of interest include coequidimensionality, (universal) catenarity, (stably strong) S-domain, and (locally, residually, totally) Jaffard domain. Positive results, leading to new examples of rings with some of the above properties, are obtained in case (the quotient group of) S has rank 1 or S is finitely generated. An example shows that some results do not carry over in case S has rank 2 but is not finitely generated.