On Certain Cross Varieties of Aperiodic Monoids with Commuting Idempotents

Authors

Edmond W. H. Lee, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

11-1-2014

Publication Title

Results in Mathematics

Keywords

Monoid, Aperiodic monoid, Commuting idempotents, Cross varieties, Variety

ISSN

1422-6383

Volume

66

Issue/No.

3

First Page

491

Last Page

510

Abstract

Let A_com denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of A_com that satisfies the identity x²yx ≈ xyx² is Cross if and only if it excludes the almost Cross varieties J₁, J₂, and L. Consequently, these three almost Cross varieties are unique among all subvarieties of A_com that satisfy the identity x²yx ≈ xyx². On the other hand, the existence of almost Cross subvarieties of A_com different from J₁, J₂, and L is also established.

Comments

Mathematics Subject Classification (2010)

20M07

NSUWorks Citation

Lee, Edmond W. H., "On Certain Cross Varieties of Aperiodic Monoids with Commuting Idempotents" (2014). Mathematics Faculty Articles. 15.
https://nsuworks.nova.edu/math_facarticles/15

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1007/s00025-014-0390-6