Study On Two Kinds Of κ-type Partial One-one Transformation Semigroups

Let natural number n>3,Xn={1,2,…,n}.Ck、CkIn and SOInk are respectively k-local cyclic groups,partial one-to-one transformation semigroups with k-local cyclic groups and partial one-to-one transformation semigroups of the ordering-preserving and k-local of descending-preserving on Xn.For an arbitrary integer r such that 0<r<n.let SI(n,r)={α∈CkIn:|im(α)|≤r},CkIr=Ck∪SI(n,r)respectively be ideal and union ideal of the semigroup CkIn.By analyzing the elements of rank r and Green-relations,the rank and the Green-relations of CkIn are obtained.Furthermore,the complete classification of(completely)isolated subsemigroups of CkIn and union ideal CkIr of CkIn are obtained,respectively.For an arbitrary integer r such that 0≤r≤n-1.By analyzing the elements of rank r and Green-relations,the Green(*)-relations and the rank of the semigroup SOInk are obtained,respectively.