It would be a subset of geometric algebra. Geometric Algebra is more generic as it defines signature e_i * e_i := {-1,0,1} (where e_i are unit vectors) and defi

It would be a subset of geometric algebra. Geometric Algebra is more generic as it defines signature e_i * e_i := {-1,0,1} (where e_i are unit vectors) and defines an exterior algebra [1]. So a 1 Dimensional geometric algebra with the signature e_1e_1 = ee := 0 is isomorphic to dual numbers. [1] https://en.wikipedia.org/wiki/Exterior_algebra https://en.wikipedia.org/wiki/Exterior_algebra