Pretzel Monoids
Year: 2025
Type: article
Abstract: We introduce an interesting class of left adequate monoids which we call pretzel monoids. These, on the one hand, are monoids of birooted graphs with respect to a natural ‘glue-and-fold’ operation, and on the other hand, are shown to be defined in the category of left adequate monoids by a natural class of presentations. They are also shown to be the free idempotent-pure expansions of right cancellative monoids, making them, in some sense, the left adequate analogues of Margolis–Meakin expansions for inverse monoids. The construction recovers the second author’s geometric model of free left adequate monoids when the right cancellative monoid is free.
Authors: Daniel Heath, Mark Kambites, Nóra Szakács
Institution: University of Manchester
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410243886