On the Rank and Relative Rank of Each Star Ideal of the Semigroup CPO_n
Gao Rong-hai · Journal of Southwest University · 2013
Let CPOn be the semigroup of all order-preserving and compressing partial singular transformations on the natural order set Xn={1,2,3,…,n} if n≥3,and let K*P(n,r)={α∈CPOn: |im α|≤r} be the two-sided star ideal of the semigroup CPOn if for an arbitrary integer r(0≤r≤n-1).The minimal generating set of the semigroup K*P(n,r) is discussed with the method of star Green's relations,and the rank of the semigroup K*P(n,r) is determined.Furthermore,the relative rank of the semigroup K*P(n,r) with respect to its star ideal K*P(n,l) for 0≤l≤r is proved.