半群POPIn^k的主因子的秩

RANK OF PRINCIPAL FACTORS OF THE SEMIGROUP POPIn^k

设自然数n≥3,POPIn是有限链[n]上的方向保序一一奇异变换半群.通过分析秩为r(0<r<n)的元素和格林关系,利用蛋壳图的方法,获得了半群POPIn^ k ={α∈POPI n:(x∈[n])x≤k xα≤k}的极小生成集,并确定了其主因子的秩.本文从变换半群的内部结构与性质去考察半群的结构与性质,在这个过程中进一步推导出了方向保序一一奇异变换半群的子半群的重要性质.

Let POPI n be the orientation-preserving injective partial transformation semigroup on[n](n≥3).By analyzing the elements of rank r and Green′s relation using egg box picture,the minimal generating set of semigroup POPIn^ k={α∈POPI n:(x∈[n])x≤k xα≤k}is obtained and the rank of its principal factor is determined.In this paper,the structure and properties of semigroups are examined from the internal structure and the properties of the transformation semigroups,further direction is deduced in the process of the orientation preserving injective partial transformation semigroups of subsemigroup important conclusions.