Semigroups of Orientation-preserving Transformations Generated by Idempotents of Rank r
Ping Zhao · Advances in Mathematics · 2010
Let SOP_n be the singular orientation-preserving semigroup on[n].In the paper we show that SOP_n is generated by idempotents of rank n—1,and its rank and idempotent rank are n.We also consider semigroup K(n,r) = {α∈SOP_n:|im(α)\≤r}, where 2≤r≤n—2,and show that K(n,r) is generated by idempotents of rank r.