Special numbers, special quaternions and special symbol elements

TL;DR

This paper introduces and investigates properties of special numbers, quaternions, and symbol elements defined by specific parameters, culminating in the construction of an algebraic structure incorporating these elements.

Contribution

It defines new classes of numbers, quaternions, and symbol elements based on parameters, and establishes an algebraic structure integrating these elements.

Findings

Defined new classes of special numbers, quaternions, and symbol elements.

Established properties and relationships among these elements.

Constructed an algebraic structure encompassing these elements.

Abstract

{\small In this paper we define and we study properties of} $\left(l,1,p+2q,q\cdot l\right) -$ {\small numbers,} $\left(l,1,p+2q,q\cdot l\right) -$ {\small quaternions,} $\left(l,1,p+2q,q\cdot l\right) -$ {\small symbol elements. Finally, we obtain an algebraic structure with these elements.}