What is the combination of Complex, Split-Complex and Dual Numbers If $a+bi:i^2=-1$ is a complex number, $a+cj:j^2=+1$ is a split-complex number, and $a+d\epsilon:\epsilon^2=0$ is a dual number; what is the term for the combination $a+bi+cj+d\epsilon:i^2=-1,j^2=+1,\epsilon^2=0$?

There is no special term as far as I know. You can call them hypercomplex numbers deffiened by certain Clifford algebra $  \mathcal{Cl} (1,1,1)$ .
