The algebra of rewriting for presentations of inverse monoids

N. D. Gilbert, E. A. McDougall

Research output: Contribution to journalArticle

13 Downloads (Pure)

Abstract

We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an example of which now arises as the fundamental groupoid of our version of the Squier complex. A further key ingredient is the factorization of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. The relation module of a presentation is then defined as the abelianized kernel of this idempotent separating map. We then use the properties of idempotent separating maps to derive a free presentation of the relation module. The construction of its kernel–the module of identities–uses further facts about pseudoregular groupoids.

Original languageEnglish
Pages (from-to)2920-2940
Number of pages21
JournalCommunications in Algebra
Volume48
Issue number7
Early online date17 Feb 2020
DOIs
Publication statusPublished - 2 Jul 2020

Keywords

  • Crossed module
  • groupoid
  • inverse monoid
  • presentation

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'The algebra of rewriting for presentations of inverse monoids'. Together they form a unique fingerprint.

  • Cite this