方向保序变换半群K(n,r)的极大正则子半群

设OP_n是［n］上的方向保序变换半群. 对任意的2≤r≤n-1, 研究半群K(n,r)={α∈OP_n: | Im(α) |≤r}极大正则子半群的结构, 利用Miller-Clifford定理, 证明了半群K(n,r)的极大正则子半群有且仅有两类： M(α)=K(n,r-1)∪(J_r＼R_α), α∈J_r; N(α)=K(n,r-1)∪(J_r＼L_α), α∈J_r, 其中: J_r={α∈OP_n: | Im(α) |=r}; R_α和L_α分别表示α所在R-类和L-类.

Maximal Regular Subsemigroups of Orientation-Preserving Transformation Semigroups K(n, r)

Let OP_n be the orientation preserving semigroup on ［n］. For an arbitrary integer r such that 2≤r≤n-1, the structures of the maximal regular subsemigroups of the semigroup K(n,r) were studied. Using Miller Clifford theorem, the authors have proved thatK(n,r) has exactly two classes of maximal regular subsemigroups, i.e.:M(α)=K(n,r-1)∪(J_r＼R_α); N(α)=K(n,r-1)∪(J_r＼L_α), α∈J_r, where J_r={α∈OP_n:| Im(α)|=r}, α∈J_r, R_α and L_α are the R class and L class containing α, respectively.