一个变换半群的同余(英文)

Some Congruences on a Transformation Semigroup

摘要: 设X是一个集合,|X|3,TX为集合X上的全变换半群.设E为X上的一个等价关系,TE(X)=f∈TX:(x,y)∈E■(f(x),f(y))∈E为由等价关系E决定的TX的一个子半群.记T2(X)=f∈TE(X):|f(X)|≤2∪id,这里id表示X上的恒等映射,则T2(X)是TE(X)的一个子半群.另外还描述了半群T2(X)上的几个同余.

Abstract: 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.