中文摘要：

Xn是包含n个元素的全序集,SPn-是Xn上的降序严格部分变换半群,对4 n和2≤r≤n-2,证明了半群SK-（n,r）={α∈SPn-∶｜Imα｜≤r}是幂等元生成的,并且是由顶端Jr＊的（r＋1）S（n,r＋1）个幂等元生成.

英文摘要：

Let SP-n be the decreasing-order strictly partial transformations on a totally ordered finite set Xn.For 4≤n,2≤r≤n-2,the paper shows that the subsemigroup SK-（n,r）={α∈SP-n∶｜Im α｜≤r}is idempotent-generated and it is generated by the（r＋1）S（n,r＋1） idempotents in J＊r.