Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over <i>Z_p</i>

Abstract

In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt plain texts, by using invertible elements in some of these algebras.

Keywords

• k-potent elements
• algebras obtained by the Cayley–Dickson process
• quaternion Fibonacci elements