Vítor H. Fernandes

Semigroups of order preserving mappings on a finite chain: A new class of divisors

In this paper we aim to prove that every semigroup of the pseudovariety generated by all semigroups of partial, injective and order preserving transformations on a finite chain belongs to the pseudovariety generated by all semigroups of order preserving mappings on a finite chain.

The monoid of all injective orientation preserving partial transformations on a finite chain

In this paper we study several structural properties of the monoids POPIn of all injective orientation preserving partial transformations on a chain with n elements: we establish descriptions for the ideals and for the congruences of these monoids and we show that POPIn is a 2-generated semigroup, for all n∈ N. Our main aim is to give a presentation for these monoids.

Presentations for some monoids of partial transformations on a finite chain: a survey

In this paper we calculate presentations for some natural monoids of transformations on a chain Xn = 1 < 2 < · · · < n . First we consider n [ n], the monoid of all full [partial] transformations on Xn that preserve or reverse the order. Two other monoids of partial transformations on Xn we look at are n and n—the elements of the first preserve the orientation and the elements of the second preserve or reverse the orientation.

PRESENTATIONS FOR SOME MONOIDS OF PARTIAL TRANSFORMATIONS ON A FINITE CHAIN

ABSTRACT In this paper we calculate presentations for some natural monoids of transformations on a chain X n = {1 < 2 <⋅s < n}. First we consider 𝒪𝒟 n [𝒫𝒪𝒟 n ], the monoid of all full [partial] transformations on X n that preserve or reverse the order. Two other monoids of partial transformations on X n we look at are 𝒫𝒪𝒫 n and 𝒫𝒪ℛ n –-the elements of the first preserve the orientation and the elements of the second preserve or reverse the orientation.

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

This paper is mainly dedicated to describing the congruences on certain monoids of transformations on a finite chain

Normally Ordered Inverse Semigroups

X_n

On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range

with

Automorphisms of partial endomorphism semigroups

n

Abelian kernels, solvable monoids and the abelian kernel length of a finite monoid

elements. Namely, we consider the monoids

The Ranks of Ideals in Various Transformation Monoids

\od_n