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

2024/05/30 by Milo Edwardes, Edwardes, Milo, Daniel J. Heath +1
Computer Science · Mathematics · #20M10 #Advanced Algebra and Logic #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2405.20197

openalex publication_date 2024/05/30 · openalex created_date 2024/06/02 · openalex updated_date 2026/07/28

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 M_n of cancellative monoids which are not group-embeddable, originating from Malcev's original work. We show that M_n 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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