The Dimension of One-step Idempotent Right Modular Quasigroups

TL;DR

This paper investigates a specific class of algebraic structures called one-step idempotent right modular quasigroups, establishing their properties, defining their dimension, and classifying those with small dimensions.

Contribution

It proves that these groupoids are quasigroups, introduces the concept of their dimension, and classifies all such quasigroups of dimensions 2, 3, and 4.

Findings

One-step idempotent right modular groupoids are quasigroups.

The dimension of these quasigroups is defined.

All quasigroups of dimensions 2, 3, and 4 are classified.

Abstract

We prove that one-step idempotent right modular groupoids are quasigroups. The dimension of such quasigroups is defined and all such quasigroups of dimensions 2,3 and 4 are determined.