Artin’s Equivalence Generalized

Abstract.

Let S be a residuated commutative monoid. Artin’s classical equivalence is related to a semigroup homomorphism of S onto the group of divisorial elements in case these form a group. An equivalence relation is considered that is more general than Artin’s equivalence. We introduce relatively divisorial elements and proceed to investigate conditions which ensure that S admits a homomorphism onto the semigroup of relatively divisorial elements when this semigroup is a Clifford monoid.