TY: JOUR
T1 - On Semigroups of Orientation-preserving Transformations with Restricted Range
A1 - Fernandes, Vitor H.
A1 - Honyam, Preeyanuch
A1 - Quinteiro, Teresa M.
A1 - Singha, Boorapa
N2 - Let Xn be a chain with n elements (n ? ?), and let ??n be the monoid of all orientation-preserving transformations of Xn. In this article, for any nonempty subset Y of Xn, we consider the subsemigroup ??n(Y) of ??n of all transformations with range contained in Y: We describe the largest regular subsemigroup of ??n(Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type ??n(Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid ??n of all either orientation-preserving or orientation-reversing transformations of Xn.
UR - http://repositorio.ipl.pt/handle/10400.21/7503
Y1 - 2016
PB - Taylor & Francis