On the axioms defining a quadratic Jordan division algebra

TL;DR

This paper demonstrates that the strict identities defining quadratic Jordan division algebras are unnecessary, broadening the understanding of their foundational axioms.

Contribution

It proves that quadratic Jordan division algebras do not require the strictness condition for their defining identities.

Findings

Strictness is not necessary for quadratic Jordan division algebras.

The axioms can be relaxed without losing algebraic properties.

This result simplifies the theory of quadratic Jordan division algebras.

Abstract

Quadratic Jordan algebras are defined by identities that have to hold strictly, i.e that continue to hold in every scalar extension. In this paper we show that strictness is not required for quadratic Jordan division algebras.