Idempotent Rank in Decreasing-Order Finite Partial Transformation Semigroups
Bo Jun Xu · Journal of Southwest University · 2008
Let Pn be a semigroup consisting of all partial transformations on a totally ordered finite set Xn.Let SPn=Pn\Sn and SP-n={α∈SPn:x∈dom α,xα≤x}.Then SP-n is a subsemigroup of all decreasing maps of SPn.In this paper it is shown that SP-n is idempotent-generated and it is generated by the n(n+1)/2 idempotents in Jn-1.