Mathematics Faculty Articles

Title

Inherently Non-Finitely Generated Varieties of Aperiodic Monoids with Central Idempotents

Document Type

Article

Publication Date

9-1-2015

Publication Title

Journal of Mathematical Sciences

Keywords

Monoid, Aperiodic monoid, Central idempotent, Variety, Finitely generated, Inherently non-finitely generated

ISSN

1072-3374

Volume

209

Issue/No.

4

First Page

588

Last Page

599

Abstract

Let A denote the class of aperiodic monoids with central idempotents. A subvariety of A that is not contained in any finitely generated subvariety of A is said to be inherently non-finitely generated. A characterization of inherently non-finitely generated subvarieties of A, based on identities that they cannot satisfy and monoids that they must contain, is given. It turns out that there exists a unique minimal inherently non-finitely generated subvariety of A, the inclusion of which is both necessary and sufficient for a subvariety of A to be inherently non-finitely generated. Further, it is decidable in polynomial time if a finite set of identities defines an inherently non-finitely generated subvariety of A.

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1007/s10958-015-2515-1

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Peer Reviewed

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