中文摘要：

设[n]={1,2,…,n}是正自然数集,Cn和PCn分别为[n]上的保序且降序变换半群和保序且降序部分变换半群.记SPCn=PCn／Cn.对n≥5,证明了半群SPCn的秩为n^2-n＋1.

英文摘要：

Let[n]= {1,2,…,n}be a natural order set,Cn and PCn be the semigroups consisting of order-preserving or order-decreasing transformations and partial order-preserving or order-decreasing transformations on [n],respectively.Denote SPCn=PCn／Cn,it is called the order-preserving and order-decreasing stricty partial transformations semigroups.For n≥5,it is given that the rank of the semigroup SPCn is n^2-n＋1.