# Equidivisible pseudovarieties of semigroups

@article{Almeida2016EquidivisiblePO, title={Equidivisible pseudovarieties of semigroups}, author={Jorge Almeida and Alfredo Costa}, journal={Publicationes Mathematicae Debrecen}, year={2016}, volume={90}, pages={435-453} }

We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free profinite semigroups are equidivisible. Besides the pseudovarieties of completely simple semigroups, they are precisely the pseudovarieties that are closed under Mal'cev product on the left by the pseudovariety of locally trivial semigroups. A further characterization which turns out to be instrumental is as the non-completely simple pseudovarieties that are closed under two-sided…

## 10 Citations

Bases for pseudovarieties closed under bideterministic product

- MathematicsAlgebra universalis
- 2019

We show that if $\mathsf V$ is a semigroup pseudovariety containing the finite semilattices and contained in $\mathsf {DS}$, then it has a basis of pseudoidentities between finite products of regular…

Locally countable pseudovarieties.

- Mathematics
- 2019

The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are…

Towards a pseudoequational proof theory

- MathematicsPortugaliae Mathematica
- 2018

A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a…

The linear nature of pseudowords

- Computer Science, MathematicsPublicacions Matemàtiques
- 2019

It is shown that, in the case of the pseudovariety of aperiodic finite semigroups, the pseudoword can be recovered from the labeled linear order.

On the group of a rational maximal bifix code

- Mathematics
- 2018

Abstract We give necessary and sufficient conditions for the group of a rational maximal bifix code Z to be isomorphic with the F-group of Z∩F{Z\cap F}, when F is recurrent and Z∩F{Z\cap F} is…

Non-locality of the meet levels of the Trotter-Weil Hierarchy

- Mathematics, Computer ScienceArXiv
- 2017

We prove that the meet level $m$ of the Trotter-Weil, $\mathsf{V}_m$ is not local for all $m \geq 1$, as conjectured in a paper by Kufleitner and Lauser. In order to show this, we explicitly provide…

Continuity and Rational Functions

- Computer Science, MathematicsICALP
- 2017

The decidability of continuity for functional transducers and some standard classes of regular languages is reported on.

Iterated morphisms, combinatorics on words and symbolic dynamical systems. (Morphismes itérés, combinatoire des mots et systèmes dynamiques symboliques)

- Computer Science
- 2019

The main subject of the thesis is the recognizability of words generated by primitive morphisms, using a coherent model of combinatorics on words and symbolic dynamical systems.

Continuity of Functional Transducers: A Profinite Study of Rational Functions

- Computer Science, MathematicsLog. Methods Comput. Sci.
- 2020

A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of…

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