Integral Domains With a Free Semigroup of *-Invertible Integral *-Ideals

Abstract

Abstract. Let * be a star-operation on an integral domain R, and let I + * (R) be the semigroup of * -invertible integral * -ideals of R. In this article, we introduce the concept of a * -coatom, and we then characterize when I + * (R) is a free semigroup with a set of free generators consisting of * -coatoms. In particular, we show that I + * (R) is a free semigroup if and only if R is a Krull domain and each v-invertible v-ideal is * -invertible. As a corollary, we obtain some characterizations of * -Dedekind domains.