Regularity and Green's Relations for a Semigroup of Transformations Preserving an Equivalence Relation
Pei Huisheng · Journal of Xinyang Normal University · 2012
Let X be a set with |X|3,TX the full transformation semigroup on X,E an equivalence relation on X and TE(X) the subsemigroup of TX determined by E which satisfies (x,y)∈E,(f(x),f(y))∈E.Let T2(X) be a subsemigroup of TE(X) and f∈T2(X),|f(X)|≤2.The Green's relations and regular elements in the semigroup T2(X) are described and discussed.