Abundant Semigroups of Transformations Preserving an Equivalence Relation
Pei Huisheng, Huijuan Zhou · Algebra Colloquium · 2011
Let X be a set with |X| ≥ 3, [Formula: see text] the full transformation semigroup on X, and E an equivalence relation on X. Let TE(X) be the set of transformations f in [Formula: see text] which preserve E, i.e., (x,y) ∈ E implies (f(x),f(y)) ∈ E. It is known that TE(X) is a subsemigroup of [Formula: see text]. In this paper, we describe the equivalence relations E so that the semigroup TE(X) is abundant.