Resumen de The class semigroup of local one-dimensional domains

Paolo Zanardo

• Let R be a local one-dimensional domain. We investigate when the class semigroup of R is a Clifford semigroup. We make use of the Archimedean valuation domains which dominate R, as a main tool to study its class semigroup. We prove that if is Clifford, then every element of the integral closure of R is quadratic. As a consequence, such an R may be dominated by at most two distinct Archimedean valuation domains, and coincides with their intersection. When is Clifford, we find conditions for to be a Boolean semigroup. We derive that R is almost perfect with Boolean class semigroup if, and only if R is stable. We also find results on , through examination of and , where V dominates R, and P, are the respective maximal ideals.