On Generalised Inflations of Right Modular Groupoids

TL;DR

This paper investigates the properties of right modular groupoids, showing that under certain conditions, their generalized inflations are equivalent to inflations, thus extending the understanding of their algebraic structure.

Contribution

It proves that right modular groupoids with cancellativity or a left identity have generalized inflations that are actually inflations, clarifying their structural relationship.

Findings

Generalized inflations of certain right modular groupoids are inflations.

Cancellative right modular groupoids have this inflation property.

Presence of a left identity ensures the same inflation equivalence.

Abstract

We prove that if a right modular groupoid U is cancellative or has a left identity then a right modular generalised inflation of U is an inflation of U.