摘要
设T_X为X上的全变换半群,E为X上的等价关系,令T_E(X)={f∈T_X:■(x,y)∈E,(f(x),f(y))∈E},则T_E(X)是T_X的子半群,如果X是一个全序集,E是X上的一个凸等价关系,设OP_E(X)为T_E(X)中所有保向映射作成的半群。对于有限全序集X上一类特殊的凸等价关系E,本文刻画了半群OP_E(X)的正则元的特征,并且描述了这个半群上的Green关系。
Let Tx be the full transformation semigroup on a set X, and E an equivalence on X. Let TE（X）={f∈Tx：↓A（X,Y）∈E,（f（X）,F（y））∈E} Then Te（X） forms a subsemigroup of Tx.If X is a totally ordered set and E is a convex equivalence on X, then let OPt（X） be a semigroup consisting of all the orientation-preserving maps in TE（X）. In this paper, for the special convex equivalence E on a finite totally ordered set X,we describe the regular elements and characterize Green＇s relations on the semigroup OPE（ X ） .
基金
河南省自然科学基金(0511010200).
关键词
变换半群
等价关系
正则元
Green关系
保向映射
transformation semigroup
equivalence
regular element
Green＇s relations
orientation-preserving map.
