Abundance of Semigroups of Transformations Restricted by an Equivalence
Lei Sun, Limin Wang · Communications in Algebra · 2016
Let σ be an equivalence on X, and let E(X, σ) denote the semigroup (under composition) of all f: X → X such that σ ⊆ ker(f). In this article, we show that the semigroup E(X, σ) is right abundant but not left abundant whenever |X| ≥3 and σ is non-trivial.