半群G(n,r)的秩和(0,1)-平方幂等元秩

On the rank and (0,1)-square idempotent rank of the semigroup G(n,r)

引入了保升序且保序有限部分一一奇异变换半群,通过对其(0, 1)-平方幂等元和星格林关系的分析,分别获得了半群G (n, r)唯一的极小(0, 1)-平方幂等元生成集,秩和(0, 1)-平方幂等元秩.进一步确定了当0≤l≤r 时,半群G (n, r)关于其星理想G (n, l)的相关秩.

We introduce one-to-one singular transformation semigroup of ascending-preserving finite parts,By analyzing the (0, 1)-square idempotent elements and star Green’s relations, the unique minimal (0, 1)-square Idempotent generating set, rank and (0, 1)-square Idempotent rank of the semigroup G(n, r) areobtained,respectively. Furthermore, the relative rank of the semigroup G(n, r) with respect to itself each star ideal G(n, l) is determined if 0 ≤ l ≤ r..