Graphical and Computational Analysis of Cayley-Dickson Algebra Elements over Zp

Abstract

 In order to determine the number of idempotent, nilpotent, and zero Divisors inside this algebraic structure, this research work gives a thorough Study of Cayley Dickson algebra over   . We also look at how many unit components there are in the algebra and offer a basic method for figuring out how many units are often present. We write pseudo code and techniques that may be used to locate these algebraic components in order to make actual implementation easier. Furthermore, we create a graphical depiction of the idempotent, nilpotent, zero divisor and units using MATLAB. By utilizing these discoveries, we expand knowledge in the area of Cayley Dickson algebras and offer an important resource for future study and application in related fields. The computed result are useful in Time like, light like and space like.