Values for the levels and sublevels of algebras obtained by the Cayley-Dickson process

TL;DR

This paper demonstrates that for any positive integer, there exists an algebra constructed via the Cayley-Dickson process over some field, which has that integer as its level.

Contribution

It establishes that all positive integers can be realized as levels of Cayley-Dickson algebras over appropriate fields, expanding understanding of algebraic structures.

Findings

Any positive integer n can be realized as the level of a Cayley-Dickson algebra.

The paper provides a method to construct such algebras for any given n.

It broadens the classification of levels in Cayley-Dickson algebras.

Abstract

In this paper we will prove that any number n\in N-{0} could be realised as level of an algebra obtained by the Cayley-Dickson process over a suitable field.