On the Complete Join of Permutative Combinatorial Rees–Sushkevich Varieties

Authors

Edmond W. H. Lee, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

2007

Publication Title

International Journal of Algebra

Keywords

Semigroups, Varieties, Rees-Sushkevich, Permutative

ISSN

1312-8868

Volume

1

Issue/No.

1

First Page

1

Last Page

9

Abstract

A semigroup variety is a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. The collection of all permutative combinatorial Rees–Sushkevich varieties constitutes an incomplete lattice that does not contain the complete join J of all its varieties. The objective of this article is to investigate the subvarieties of J. It is shown that J is locally finite, non-finitely generated, and contains only finitely based subvarieties. The subvarieties of J are precisely the combinatorial Rees–Sushkevich varieties that do not contain a certain semigroup of order four.

Comments

Mathematics Subject Classification: 20M07, 08B15

Creative Commons License

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

NSUWorks Citation

Lee, Edmond W. H., "On the Complete Join of Permutative Combinatorial Rees–Sushkevich Varieties" (2007). Mathematics Faculty Articles. 139.
https://nsuworks.nova.edu/math_facarticles/139

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.12988/ija.2007.07001