On definition of CI-quasigroup

TL;DR

This paper introduces the concept of CI-quasigroups, a type of groupoid satisfying a specific identity involving a map J, expanding the understanding of algebraic structures with particular properties.

Contribution

It formally defines CI-quasigroups based on a new identity involving a map J, contributing to the classification of algebraic structures.

Findings

Defined CI-quasigroup via a specific identity

Characterized properties of CI-quasigroups

Extended algebraic structure classifications

Abstract

Groupoid $(Q, \cdot)$ in which equality $(xy)Jx = y$ is true for all $x, y \in Q$, where $J$ is a map of the set $Q$, is a CI-quasigroup.