A collection of cancellative, singly aligned, non-group embeddable monoids
Year: 2025
Type: article
Abstract: By classical results of Malcev, cancellative monoids need not be group-embeddable. We describe, give presentations for and study an infinite family $${\mathcal {M}}_n$$ M n of cancellative monoids which are not group-embeddable, originating from Malcev’s work. We show that $${\mathcal {M}}_n$$ M n is singly aligned for $$n \ge 2$$ n ≥ 2 , owing to applications in the study of $$\textrm{C}^*$$ C ∗ -algebras by Brix, Bruce and Dor-On. We finish by showing that $${\mathcal {M}}_1$$ M 1 is not singly aligned, but 2-aligned.
Source: Semigroup Forum
Authors: Milo Edwardes, Daniel Heath
Institution: University of Manchester
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4408044088