半群SPO_(n)^(k)的格林(星)关系及富足性

The(star)Green’s relations and abundance of the semigroup SPO_(n)^(k)

设自然数n≥3,X_(n)={1,2,…,n}。O_(n)和PO_(n)分别是有限集X_(n)上的保序变换半群和部分保序变换半群。对1≤k≤n,记SPO_(n)=PO_(n)\O_(n),SPO_(n)^(k)={α∈SPO_(n):∀x≤k⇒xα≤k},易验证半群SPO_(n)^(k)为部分变换半群P_(n)的子半群。通过对半群SPO_(n)^(k)中的元素的分析,得到了半群SPO_(n)^(k)的格林(星)关系及非正则富足性。

Let n≥3,X_(n)={1,2,…,n}.O_(n)and PO_(n)be order-preserving transformation semigroup and partial order-preserving transformation semigroup,respectively,on finite set X_(n).For 1≤k≤n,let SPO_(n)=PO_(n)\O_(n),SPO_(n)^(k)={α∈SPO:∀x≤k⇒xα≤k}.It is to prove that SPO_(n)^(k)be subsemigroup of partial transformation semigroup P_(n).By analyzing the elements of the semigroup SPO_(n)^(k),the(star)Green’s relations and irregular abundance of the semigroup SPO_(n)^(k)is obtained,respectively.