2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137959The 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.Section 4 was removed. J. Reine Angew. Math. (to appear), 17 pagesCommutative AlgebraNumber Theory13C20; 13F05; 11R65; 11R29; 20M14text