The monoid of all orientation-preserving and extensive full transformations on a finite chain

Let [Formula: see text] be the monoid of all orientation-preserving and extensive full transformations on [Formula: see text] ordered in the standard way. In this paper, we determine the minimum generating set and the minimum idempotent generating set of [Formula: see text], and so the rank and the idempotent rank of [Formula: see text] are obtained. Moreover, we describe maximal subsemigroups and maximal idempotent generated subsemigroups of [Formula: see text] and completely obtain their classifications.

Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set

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.

Maximal subsemigroups containing a particular semigroup

We characterize maximal subsemigroups of the monoid T(X) of all transformations on the set X = ℕ of natural numbers containing a given subsemigroup W of T(X) such that T(X) is finitely generated over W. This paper gives a contribution to the characterization of maximal subsemigroups on the monoid of all transformations on an infinite set.

On Maximal Subsemigroups of Partial Baer-Levi Semigroups

Suppose thatXis an infinite set with|X|≥q≥ℵ0andI(X)is the symmetric inverse semigroup defined onX. In 1984, Levi and Wood determined a class of maximal subsemigroupsMA(using certain subsetsAofX) of the Baer-Levi semigroupBL(q)={α∈I(X):domα=Xand|X∖Xα|=q}. Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups ofBL(q), but these are far more complicated to describe. It is known thatBL(q)is a subsemigroup of the partial Baer-Levi semigroupPS(q)={α∈I(X):|X∖Xα|=q}. In this paper, we characterize all maximal subsemigroups ofPS(q)when|X|>q, and we extendMAto obtain maximal subsemigroups ofPS(q)when|X|=q.