Algebraic geometry

Residue field

In mathematics, the residue field is a basic construction in commutative algebra. If R is a commutative ring and m is a maximal ideal, then the residue field is the quotient ring k = R/m, which is a field. Frequently, R is a local ring and m is then its unique maximal ideal. This construction is applied in algebraic geometry, where to every point x of a scheme X one associates its residue field k(x). One can say a little loosely that the residue field of a point of an abstract algebraic variety is the 'natural domain' for the coordinates of the point. (Wikipedia).

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Algebraic Geometry (book) | Prime ideal | Quotient ring | Morphism of finite type | Algebraically closed field | Zariski topology | Krull dimension | Transcendence degree | Maximal ideal | Algebraic variety | Commutative algebra | Hilbert's Nullstellensatz | Field extension | Mathematics | Field (mathematics) | Generic point | Algebraic geometry | Rational point | Scheme (mathematics) | Local ring | Commutative ring