Affine ring

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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.