Let be the set of prime ideals of a commutative ring . Then an affine scheme is a technical mathematical object defined as the ring spectrum of , 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.

# Affine Scheme

## See also

Affine Variety, Prime Ideal, Ring Spectrum, Scheme
*Portions of this entry contributed by Margherita
Barile*

## Explore with Wolfram|Alpha

## 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 Scheme## Cite this as:

Barile, Margherita and Weisstein, Eric W. "Affine Scheme." From *MathWorld*--A
Wolfram Web Resource. https://mathworld.wolfram.com/AffineScheme.html