Affine ring

Definition

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