保持双向等价关系的变换半群自然偏序关系的若干结果

Some Results for the Naturally Ordered Transformation Semigroups Preserving Double Direction Equivalence

设X为任意的非空集合,T X是X上的全变换半群.设E是X上的一个等价关系,T E*(X)是由等价关系E所决定的T X的子半群,满足(x,y)∈E当且仅当(f(x),(fy))∈E.将讨论T E*(X)中的变换在自然偏序关系下的覆盖元以及任意两个变换的上(下)界.

Let X be an arbitrary nonempty set, Tx is the full transformation semigroup on X. Let E be an equivalence relation on X, TE.（X） is a subsemigroup of TX determined by E which satisfies （x,y） ∈E if and only if （f（x）, f（y） ）∈ E. In this paper, the covering elements of TE.（X） under the natural order are described, and the lower （upper） bound of two elements is discussed.