Abstract :
Let R be a local one-dimensional domain. We investigate when the class semigroup image 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 image is Clifford, then every element of the integral closure image of R is quadratic. As a consequence, such an R may be dominated by at most two distinct Archimedean valuation domains, and image coincides with their intersection. When image is Clifford, we find conditions for image 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 image, through examination of image and image, where V dominates R, and P, image are the respective maximal ideals.
