Constituent Groups of Clifford Semigroups Arising from t-Closure

Abstract

The t-class semigroup of an integral domain R, denoted S_t(R), is the semigroup of fractional t-ideals modulo its subsemigroup of nonzero principal ideals with the operation induced by ideal t-multiplication. We recently proved that if R is a Krull-type domain, then S_t(R) is a Clifford semigroup. This paper aims to describe the idempotents of S_t(R) and the structure of their associated groups. We extend and recover well-known results on class semigroups of valuation domains and Prufer domains of finite character.