Green＇s Relations on Semigroups of Transformations Preserving Two Equivalence Relations

摘要

Let TX be the full transformation semigroup on a set X.For a non-trivial equivalence F on X,let TF(X) = {f ∈ TX :(x,y) ∈ F,(f(x),f(y)) ∈ F}.Then TF(X) is a subsemigroup of TX.Let E be another equivalence on X and TFE(X) = TF(X) ∩ TE(X).In this paper,under the assumption that the two equivalences F and E are comparable and E ■ F,we describe the regular elements and characterize Green's relations for the semigroup TFE(X).