New Results on Generalized Quaternion Algebra Involving Generalized Pell-pell Lucas Quaternions

Abstract

his work presents a new sequence, generalized Pell-Pell-Lucas quaternions, we prove that the set of these elements forms an order of generalized quaternions with 3-parameters kλ1,λ2,λ3 as defined by ring theory. In addition, some properties of these elements are presented. The properties in this article refer to kλ1,λ2,λ3 algebras and sometimes to the 2-parameter algebra H(α, β).