On a Semigroup Variety of György Pollák

Authors

Edmond W. H. Lee, Simon Fraser UniversityFollow

Document Type

Article

Publication Date

2010

Publication Title

Novi Sad Journal of Mathematics

Keywords

Semigroups, Varieties, Quasilinear varieties, Finitely generated

ISSN

1450-5444

Volume

40

Issue/No.

3

First Page

67

Last Page

73

Abstract

Let P be the variety of semigroups defined by the identity xyzx = x². By a result of György Pollák, every subvariety of P is finitely based. The present article is concerned with subvarieties of P and the lattice they constitute, where the main result is a characterization of finitely generated subvarieties of P. It is shown that a subvariety of P is finitely generated if and only if it contains finitely many subvarieties, and the identities defining these varieties are described. Specifically, it is decidable when a finite set of identities defines a finitely generated subvariety of P. It follows that the finitely generated subvarieties of P constitute an incomplete lattice while the non-finitely generated subvarieties of P constitute an interval. It is also shown that given any pair of finitely generated subvarieties of P, a finite semigroup that generates their meet is computable.

Comments

AMS Mathematics Subject Classification (2010): 20M07

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

NSUWorks Citation

Lee, Edmond W. H., "On a Semigroup Variety of György Pollák" (2010). Mathematics Faculty Articles. 151.
https://nsuworks.nova.edu/math_facarticles/151

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013