有向路上的保向部分一一变换半群

Semigroup of all orienation-preserving partial ingeatuie transformation on a finite path

设In是集Xn={1,2,3,…,n}上的对称逆半群,且有向路为ρ={(1,2),(2,3),(3,4),…,(n-1,n)},令Iρ={α∈In:x,y∈dom,α(x,y)∈ρ■(xα,yα)∈ρ}∪{φ}.证明了Iρ是一个类A子半群,研究了Iρ的Green*-关系,进一步得到Ip的*理想.

Abstract： Let In be a symmetric inverse subsemigroup on the set Xn={1,2,3…,n},and ρ={（1,2）,（2,3）,（3,4）…（n-1,n）} a directed path.Let Iρ={α∈In：arbitaryx,y∈dom α,（x,y）∈ρ→（xα,yα）∈ρ}∪{Ф}.It was proved Iρ was a type A subsemigroup of In , furthermore the Green ＊ -relations of Iρ was investigated and the ＊ -ideal of Iρ was obtained.