  The t-class semigroup of an integral domain is the semigroup of the isomorphy
classes of the t-ideals with the operation induced by ideal t-multiplication.
This paper investigates ring-theoretic properties of an integral domain that
reflect reciprocally in the Clifford or Boolean property of its t-class
semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that
suit best t-multiplication are studied in an attempt to generalize well-known
developments on class semigroups. We prove that a Prufer v-multiplication
domain (PVMD) is of Krull type (in the sense of Griffin) if and only if its
t-class semigroup is Clifford. This extends Bazzoni and Salce's results on
valuation domains and Prufer domains. We also characterize GCD domains with
Boolean t-class semigroup, recovering thus recent results on Bezout domains.
