Maximal regular subsemigroups of the ideals of semigroup POP_n
Yuanqi Zhao · Journal of Northeast Normal University · 2015
Let Xn= {1,2,…,n},ordered in the standard way.Let POPnbe the partial orientationpreserving transformation semigroup on Xn.For an arbitrary integer r such that 2≤r≤n-1,the structures of the maximal regular subsemigroups of the semigroup POP(n,r)={α∈POPn:|im(α)|≤r}were studied.Using Miller-Clifford theorem,the authors have proved that POP(n,r)has exactly a class of maximal regular subsemigroups,Mα=POP(n,r-1)∪(Jr\Rα),α∈J,where J={α∈POPn:|im(α)|=r},Rαbe the R-class containingα.