Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1305-2036-6 |
Объём: | 68 страниц |
Масса: | 123 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
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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