Mathematics Faculty Articles

Title

Join irreducible 2-testable semigroups

Document Type

Article

Publication Date

2021

Publication Title

Discussiones Mathematicae - General Algebra and Applications

Keywords

semigroup, 2-testable, pseudovariety, join irreducible

ISSN

2084-0373

Volume

41

Issue/No.

1

First Page

103

Last Page

112

Abstract

A nontrivial pseudovariety is join irreducible if whenever it is contained in the complete join of some collection of pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. The present article is concerned with semigroups that are 2-testable in the sense that they satisfy any equation formed by a pair of words that begin with the same variable,end with the same variable, and share the same set of factors of length two. The main objective is to show that there exist precisely seven join irreducible pseudovarieties of 2-testable semigroups. As a consequence, it is decidable in quadratic time if a finite 2-testable semigroup is join irreducible.

Comments

Dedicated to the 65th birthday of Professor Jorge Almeida.

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.7151/dmgaa.1354

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