Mathematics Faculty Articles

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

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.12988/ija.2007.07001

Peer Reviewed

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