ABUNDANCE OF THE SEMIGROUP OF ALL TRANSFORMATIONS OF A SET THAT REFLECT AN EQUIVALENCE RELATION
Lei Sun, Limin Wang · Journal of Algebra and Its Applications · 2013
Let [Formula: see text] be the full transformation semigroup on a nonempty set X and E be an equivalence relation on X. We write [Formula: see text] Then T∃(X) is a subsemigroup of [Formula: see text]. In this paper, we proved that the semigroup T∃(X) is not abundant if X/E is infinite.