An affine scheme is the ring spectrum 
of a commutative ring 
, regarded as a local-ringed space with
a structure sheaf. Its underlying set 
consists of the prime ideals
of 
. 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.
Affine Scheme
See also
Affine Variety, Prime Ideal, Ring Spectrum, SchemePortions of this entry contributed by Margherita Barile
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References
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.Referenced on Wolfram|Alpha
Affine SchemeCite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Affine Scheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AffineScheme.html