Non-group rank and relative rank of each ideal of the semigroup PO_n
Luo Yong-gu · Journal of Northeast Normal University · 2014
Let POnbe the semigroup of all order-preserving partial singular transformations on a finitechain[n].For an arbitrary integer r(2≤r≤n-1),the non-group rank and non-idempotent rank of the semigroup M(n,r)={α∈POn:|Imα|≤r}were studied.We proved that M(n,r)is generated by elements of rank r.Furthermore,it is shown that for 0≤l≤r,the relative rank of the semigroup M(n,r)with respect to itself each ideal M(n,l).