Affine Scheme

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a local-ringed space with a structure sheaf. A local-ringed space that is locally isomorphic to an affine scheme is called a scheme (Itô 1986, p. 69). An affine scheme is a generalization of the notion of affine variety, where the coordinate ring is replaced by any commutative unit ring, and the variety with the Zariski topology is replaced by any topological space.

See also

Affine Variety, Prime Ideal, Ring Spectrum, Scheme

Portions of this entry contributed by Margherita Barile

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Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.Itô, K. (Ed.). "Schemes." §16D in Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 1. Cambridge, MA: MIT Press, p. 69, 1986.

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Affine Scheme

Cite this as:

Barile, Margherita and Weisstein, Eric W. "Affine Scheme." From MathWorld--A Wolfram Web Resource.

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