Maximal Regular Subsemigroups of Orientation-Preserving Transformation Semigroups K(n,r)
Bo Jun Xu · Journal of Jilin University(Science Edition) · 2011
Let OPn 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)∪(Jr\Rα);N(α)=K(n,r-1)∪(Jr\Lα),α∈Jr,where Jr={α∈OPn: Im(α)=r},α∈Jr,Rα and Lα are the R-class and L-class containing α,respectively.