Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
Tiwadee Musunthia, Jörg Koppitz · Forum Mathematicum · 2016
Abstract In this paper, we study the maximal subsemigroups of several semigroups of order-preserving transformations on the natural numbers and the integers, respectively. We determine all maximal subsemigroups of the monoid of all order-preserving injections on the set of natural numbers as well as on the set of integers. Further, we give all maximal subsemigroups of the monoid of all bijections on the integers. For the monoid of all order-preserving transformations on the natural numbers, we classify also all its maximal subsemigroups, containing a particular set of transformations.