Some remarks regarding l elements defined in algebras obtained by the Cayley-Dickson process

TL;DR

This paper introduces a special class of elements called l elements in Cayley-Dickson algebras, providing conditions for their invertibility to aid in discovering new algebraic identities.

Contribution

It defines l elements in Cayley-Dickson algebras and establishes invertibility conditions, advancing understanding of algebraic identities and properties.

Findings

Defined l elements in Cayley-Dickson algebras

Derived conditions for invertibility of l elements

Potential applications in discovering new algebraic identities

Abstract

In this paper, we define a special class of elements in the algebras obtained by the Cayley Dickson process, called l elements. We find conditions such that these elements to be invertible. These conditions can be very useful for finding new identities, identities which can help us in the study of the properties of these algebras.