  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.
