affine algebra  Given a field k an affine algebra is any
finitely generated noetherian associative commutative unital
k-algebra without nilpotent elements. This term is limited to a
small community of algebraists and may bring confusion if quoted
outside of that context. The name is from the fact that the
affine algebras are the coordinate rings of affine varieties;
equivalently, an affine k-variety is precisely the maximal
spectrum of an affine k-algebra.