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 grou p rings, results are sought for a number of properties of the semigrou p ring A[S]. The properties of interest include coequidimensionality, (universal) catenarity, (stably strong) S-domain, and (locally, residu ally, totally) Jaffard domain. Positive results, leading to new exampl es of rings with some of the above properties, are obtained in case (t he quotient group of) S has rank 1 or S is finitely generated. An exam ple shows that some results do not carry over in case S has rank 2 but is not finitely generated.