On Idempotent Ranks of Semigroup PO_n(k)
LI Xian-chon · Journal of Southwest China Normal University · 2013
Let POn be the semigroup of all order-preserving partial transformations on[n].In the paper we consider semigroup POn(k)={α∈POn:■x∈dom(α),x≤k■xα ≤k},where 1≤k≤n-1,and show that POn(k)is generated by idempotents of rank n-1 and its idempotent rank and rank are equal to 3n-3 and 2n-1,respectively.