Some Results for Semigroups of Transformations Preserving Double Direction Equivalence
Weina Deng · Journal of Southwest University · 2012
Let X be an arbitrary set and E an equivalence relation on X.Let TX denote the full transformation semigroup on X and TE*(X)={f∈TX: *x,y∈X,(x,y)∈E if and only if(f(x),f(y))∈E}.Then TE*(X) is a subsemigroup of TX.In this paper,we investigate the conditions under which TE*(X) is abundant.Also,we describe the equivalence relation E for which D=J in TE*(X).