A collection of cancellative, singly aligned, non-group embeddable monoids

Milo Edwardes; Daniel Heath

doi:10.1007/s00233-025-10509-2

A collection of cancellative, singly aligned, non-group embeddable monoids

Milo Edwardes, Daniel Heath

Department of Mathematics

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Abstract

By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family Mn of cancellative monoids which are not group-embeddable, originating from Malcev's original work. We show that Mn is singly aligned for n ≥ 2, owing to applications in the study of C∗-algebras by Brix, Bruce and Dor-On. We finish by showing that M1 is not singly aligned, but is 2-aligned.

Original language	English
Pages (from-to)	296–307
Journal	Semigroup Forum
Volume	110
Early online date	28 Feb 2025
DOIs	https://doi.org/10.1007/s00233-025-10509-2
Publication status	Published - 1 Apr 2025

Keywords

math.RA
math.OA
20M10

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10.1007/s00233-025-10509-2Licence: CC BY

Cite this

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abstract = "By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family Mn of cancellative monoids which are not group-embeddable, originating from Malcev's original work. We show that Mn is singly aligned for n ≥ 2, owing to applications in the study of C∗-algebras by Brix, Bruce and Dor-On. We finish by showing that M1 is not singly aligned, but is 2-aligned.",

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N2 - By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family Mn of cancellative monoids which are not group-embeddable, originating from Malcev's original work. We show that Mn is singly aligned for n ≥ 2, owing to applications in the study of C∗-algebras by Brix, Bruce and Dor-On. We finish by showing that M1 is not singly aligned, but is 2-aligned.

AB - By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family Mn of cancellative monoids which are not group-embeddable, originating from Malcev's original work. We show that Mn is singly aligned for n ≥ 2, owing to applications in the study of C∗-algebras by Brix, Bruce and Dor-On. We finish by showing that M1 is not singly aligned, but is 2-aligned.

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A collection of cancellative, singly aligned, non-group embeddable monoids

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Keywords

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