Abstract:

Let DO_n be the semigroup of all orderreversing  singular transformations on a finitechain ［n］. For an arbitrary integer r(1≤r≤n-1), the rank of semigroup L_D(n,r)={α∈DOn: |Im α|≤r} was studied. We proved that L_D(n,r) is generated by elements of rank r, with rank being C^r_n. Furthermore, it is shown that the relative rank of the semigroup L_D(n,r) with respect to itself each ideal L_D(n,l) is equal to C^r_n if 1≤l

Key words: orderpreserving, orderreversing, singular transformation semigroup, rank, relative rank