The zero divisors of the Cayley-Dickson algebras over the real numbers

TL;DR

This paper provides an algebraic description of zero divisors in Cayley-Dickson algebras over the real numbers for dimensions four and above, enhancing understanding of their algebraic structure.

Contribution

It offers a new algebraic characterization of zero divisors in Cayley-Dickson algebras for all dimensions n ≥ 4.

Findings

Algebraic description of zero divisors in Cayley-Dickson algebras for n ≥ 4

Extension of previous results to higher-dimensional algebras

Deeper insight into the structure of zero divisors in these algebras

Abstract

In this paper we describe algebraically the zero divirsors of the Cayley- Dickson algebras $\a_{n}=\erre^{2^n}$ for $n \ge 4$ over the real numbers.