Mathematics Faculty Articles

Varieties of Involution Monoids with Extreme Properties

Document Type

Article

Publication Date

6-22-2019

Publication Title

The Quarterly Journal of Mathematics

ISSN

0033-5606

Volume

70

Issue/No.

4

First Page

1157

Last Page

1180

Abstract

A variety that contains continuum many subvarieties is said to be huge. A sufficient condition is established under which an involution monoid generates a variety that is huge by virtue of its lattice of subvarieties order-embedding the power set lattice of the positive integers. Based on this result, several examples of finite involution monoids with extreme varietal properties are exhibited. These examples—all first of their kinds—include the following: finite involution monoids that generate huge varieties but whose reduct monoids generate Cross varieties; two finite involution monoids sharing a common reduct monoid such that one generates a huge, non-finitely based variety while the other generates a Cross variety; and two finite involution monoids that generate Cross varieties, the join of which is huge.

Comments

©The Author(s) 2019. Published by Oxford University Press. All rights reserved.

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1093/qmath/haz003

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