Abstract:

Let OP_n be the orientationpreserving semigroup on ［n］. For an arbitrary integer r such that 2≤r≤n-1, the structures of the maximal regular subsemigroups of the semigroup K(n,r) were studied.  Using MillerClifford theorem, the authors have proved thatK(n,r) has exactly two classes of maximal regular subsemigroups, i.e.:M(α)=K(n,r-1)∪(J_r＼R_α); N(α)=K(n,r-1)∪(J_r＼L_α), α∈J_r, where J_r={α∈OP_n: | Im(α)|=r}, α∈J_r, R_α and L_α are the Rclass and  L class containing α, respectively.

Key words:  transformation semigroup, orientationpreserving transformation semigroup, maximal regular subsemigroup