R.: Analytically unramified one-dimensional semilocal rings and their value semigroups

In a one-dimensional local ring R with finite integral closure each nonzerodivisor has a value in Nd, where d is the number of maximal ide-als in the integral closure. The set of values constitutes a semigroup, the value semigroup of R. We investigate the connection between the value semigroup and the ring. There is a particularly close connection for some classes of rings, e.g. Gorenstein rings, Arf rings, and rings of small multi-plicity. In many respects the Arf rings and the Gorenstein rings turn out to be opposite extremes. We give applications to overrings, intersection numbers, and multiplicity sequences in the blow-up sequences studied by Lipman.