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)

摘要: 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 \left( 0,\;1 \right)- 平方幂等元和星格林关系的分析，分别获得了半群 G\left( n,r \right) 唯一的极小 \left( 0,\;1 \right)- 平方幂等元生成集，秩和 \left( 0,\;1 \right)- 平方幂等元秩. 进一步确定了当 0 \leqslant l \leqslant r 时，半群 G\left( n,\;r \right) 关于其星理想 G\left( n,\;l \right) 的相关秩.

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