保E*关系且方向保序严格部分一一变换半群的秩
On the rank of semigroup of preserving E relation and orientation strictly partial one-one transformations

设X为有限集合，E为X上的等价关系，令SOPIE*(X)为X 上的所有保E*关系且方向保序严格部分一一变换构成的半群. 为了讨论此变换半群的秩，引入了新的等价关系从而得到新的等价类. 通过对等价类的分析得到了半群SOPIE*(X)的秩.
Let E be an equivalence relation on a finite set X. The semigroup denoted by SOPIE*(X) consisting of all preserving E* relation and orientation strictly partial one-one transformations. In order to discuss the rank of this transformation semigroup，this paper introduces some new equivalence relations to get new equivalence classes. The rank of semigroup SOPIE*(X) is obtained by analyzing the equivalence classes