一类保持等价关系的变换半群的正则性和格林关系

Regularity and Green’s Relations for a Semigroup of Transformations Preserving an Equivalence Relati

摘要: 设X为非空集合,|X|3,TX是X上的全变换半群.设E是X上的一个等价关系,TE(X)是由等价关系E所决定的TX的子半群,满足(x,y)∈E,(f(x),f(y))∈E.记T2(X)是TE(X)的一个子半群,满足f∈T2(X),|f(X)|≤2.讨论了半群T2(X)上的格林关系和正则元.

Abstract: 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.