Constituent groups of Clifford semigroups arising from t-closure

The t-class semigroup of an integral domain R, denoted St(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 [M. Griffin, Rings of Krull type, J. Reine Angew. Math. 229 (1968) 1–27], then St(R) is a Clifford semigroup [S. Kabbaj, A. Mimouni, t-Class semigroups of integral domains, J. Reine Angew. Math. 612 (2007) 213–229]. In this paper, we aim to describe the idempotents of St(R) and the structure of their associated groups. We extend and recover well-known results on class semigroups of valuation domains and Prüfer domains of finite character.