Like manifolds, schemes are defined as spaces that are locally modeled on a familiar space. In the case of manifolds, the familiar space is Euclidean space. For a scheme, the local models are called affine schemes. Affine schemes provide a direct link between algebraic geometry and commutative algebra. The fundamental objects of study in commutative algebra are commutative rings. If formula_8 is a commutative ring, then there is a corresponding affine scheme formula_9 which translates the algebraic structure of formula_8 into geometry. Conversely, every affine scheme determines a commutative ring, namely, the ring of global sections of its structure sheaf. These two operations are mutually inverse, so affine schemes provide a new language with which to study questions in commutative algebra. By definition, every point in a scheme has an open neighborhood which is an affine scheme.