Investigating generalized quaternions with dual-generalized complex numbers

summary:We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $\alpha $, $\beta $ and $\mathfrak {p}$. Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given