Class semigroups and t-class semigroups of integral domains

The class (t-class) semigroup of an integral domain is the semigroup of the isomorphy classes of the nonzero fractional ideals (t-ideals) with the operation induced by ideal (t-) multiplication. This paper surveys recent literature which studies ring-theoretic conditions that reflect reciprocally in the Clifford property of the class (t-class) semigroup. Precisely, it examines integral domains with Clifford class (t-class) semigroup and describes their idempotent elements and the structure of their associated constituent groups.