Generalized Cohn's Theorem

TL;DR

This paper generalizes Cohn's Theorem within the framework of free associative -algebras on disjoint sets, expanding the theoretical understanding of Jordan algebras.

Contribution

It introduces the concept of free associative -algebras on disjoint sets and extends Cohn's Theorem to this broader context.

Findings

Established a generalized version of Cohn's Theorem for Jordan algebras.

Defined the notion of free associative -algebras on disjoint sets.

Provided theoretical proofs and framework for the generalization.

Abstract

We introduce the notion of a free associative $\mathcal{Z}_2$-algebra on the union of two disjoint sets and prove a generalization of Cohn's Theorem on Jordan algebras.