On Semigroups of Orientation-preserving Transformations with Restricted Range
VΓtor Hugo Fernandes, Preeyanuch Honyam, Teresa M. Quinteiro, Boorapa Singha Β· Communications in Algebra Β· 2015
Let X n be a chain with n elements (n β β), and let πͺπ« n be the monoid of all orientation-preserving transformations of X n . In this article, for any nonempty subset Y of X n , we consider the subsemigroup πͺπ« n (Y) of πͺπ« n of all transformations with range contained in Y: We describe the largest regular subsemigroup of πͺπ« n (Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type πͺπ« n (Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid πͺβ n of all either orientation-preserving or orientation-reversing transformations of X n .