Prime serial rings with krull dimension

Let Abe an integral domain and Sa torsion-free can-cellative Abelian semigroup. By analogy with known results on 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 do-main. Positive results, leading to new examples of rings with some of the above properties, are obtained in case (the quotient group of) Shas rank 1 or Sis finitely generated. An example shows that some results do not carry over in case Shas rank 2 but is not finitely generated.