Mathematics Faculty Articles

Title

On Certain Cross Varieties of Aperiodic Monoids with Commuting Idempotents

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 Acom denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of Acom that satisfies the identity x2yxxyx2 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 Acom that satisfy the identity x2yxxyx2. On the other hand, the existence of almost Cross subvarieties of Acom different from J1, J2, and L is also established.

Comments

Mathematics Subject Classification (2010)

20M07

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1007/s00025-014-0390-6

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