I thought Grassmann algebra consisted of only scalars, vectors, bivectors, etc. but not their linear combinations. So a mixed scalar plus vector is not an eleme

I thought Grassmann algebra consisted of only scalars, vectors, bivectors, etc. but not their linear combinations. So a mixed scalar plus vector is not an element of a Grassmann algebra. An alternative name is exterior algebra. You get Clifford algebra / Geometric Algebra (two names for the same thing) by taking closure under sums and considering a more general product. [edit: It appears I'm right: https://en.wikipedia.org/wiki/Exterior_algebra https://en.wikipedia.org/wiki/Exterior_algebra]