Biquasigroups linear over a group

TL;DR

This paper investigates the structure of biquasigroups that satisfy certain identities, focusing on those that are linear over a group, to understand their algebraic properties.

Contribution

It characterizes biquasigroups satisfying specific identities, especially those linear over a group, expanding the understanding of their algebraic structure.

Findings

Identifies the structure of biquasigroups satisfying Polonijo's Ward identity

Classifies biquasigroups linear over a group

Provides new insights into algebraic properties of these structures

Abstract

We determine the structure of biquasigroups (Q,^,*) satisfying varations of Polonijo's Ward double quasigroup identity (x^z)*(y^z)=x*y, including those that are linear over a group.