Mathematics Faculty Articles

Title

The Smallest Monoid that Generates a Non-Cross Variety

Document Type

Article

Publication Date

1-2014

Publication Title

Journal of Xiamen University (Natural Science)

Keywords

Monoid, Variety, Cross Variety

ISSN

0438-0479

Volume

53

Issue/No.

1

First Page

1

Last Page

4

Abstract

A monoid variety is a class of monoids that is closed under the formation of homomorphic images, submonoids, and arbitrary direct products. A finitely generated, finitely based variety of monoids that contains only finitely many subvarieties is a Cross monoid variety. The 5-element monoid M5 is first shown to generate a non-Cross monoid variety. Then it is shown that, up to isomorphism and anti-isomorphism, any monoid of order five or less different from M5 generates a Cross monoid variety. Therefore up to isomorphism and anti-isomorphism, M5 is the only smallest monoid that generates a non-Cross monoid variety.

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.6043/j.issn.0438-0479.2014.01.001

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