The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain. (Q2915416)

Let \(X_n=\{1<2<\cdots<n\}\) be a finite chain with \(n\) elements, \(\mathcal{OP}_n\) (\(\mathcal{OR}_n\)) the monoid of all orientation-preserving (orientation-preserving or orientation reversing) full transformations of \(X_n\). In this paper the maximal subsemigroups of the monoids \(\mathcal{OP}_n\) and \(\mathcal{OR}_n\) and of their ideals are described.