Affine ring

Definition
Let $$R$$ be a commutative unital ring. An affine ring over $$R$$ is a ring isomorphic to $$R[x_1,x_2,\ldots,x_n]/I$$ where $$I$$ is an ideal.

When we simply say affine ring, we may mean affine ring over a field, viz affine ring where the ring $$R$$ is a field.

Facts
An affine ring over an affine ring is also an affine ring over the base field.