There is no such thing as affine algebra: https://en.wikipedia.org/wiki/Affine_algebra

There are affine spaces, and there is an algebra of the elements of affine spaces. That is, rules that describe how the elements can be manipulated. There are affine transforms, affine combinations, affine bases, and so on, all of them analogous to the corresponding concepts in linear algebra.

(The term "algebra" can also refer to a particular type of algebraic structure in math, but that’s not what I meant.)