Mathematics Faculty Articles

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

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

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

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