Some Congruences on a Transformation Semigroup
LU Feng-mei · Journal of Xinyang Normal University · 2011
Let X be a set with |X|3,TX the full transformation semigroup on X.Let E be an equivalence relation on X and TE(X)={f∈TX:(x,y)∈E■(f(x),f(y))∈E} the subsemigroup of TX determined by E.Denote T2(X)={f∈TE(X):|f(X)|≤2}∪{id},where id denotes the identity map on X.Then T2(X) is a subsemigroup of TE(X).Among other things,some congruences on the semigroup T2(X) are described.