Residue Field
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High Quality Content by WIKIPEDIA articles! 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. Suppose that R is a commutative local ring, with the maximal ideal m. Then the residue field is the quotient ring R/m.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786130520366
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786130520366
- Format Fachbuch
- Titel Residue Field
- Herausgeber Betascript Publishing
- Anzahl Seiten 68
- Genre Mathematik
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