Distributivity in Quandles and Quasigroups

TL;DR

This paper surveys the role of distributivity in algebraic structures like quasigroups and quandles, highlighting its significance across various mathematical contexts including knot theory.

Contribution

It provides a comprehensive overview of how distributivity manifests and is studied within quasigroup and quandle theories, connecting different areas of algebra.

Findings

Distributivity is fundamental in the structure of quasigroups and quandles.

The survey links distributivity to applications in knot theory.

Various types of distributive properties are explored across contexts.

Abstract

Distributivity in algebraic structures appeared in many contexts such as in quasigroup theory, semigroup theory and algebraic knot theory. In this paper we give a survey of distributivity in quasigroup theory and in quandle theory.