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 right LCM 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 right LCM, but is $2$-aligned.
No takes yet. Share an insight, caveat, or question.
Edwardes et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: