Affine variety

（重定向自Coordinate ring）

In algebraic geometry, an affine variety over an algebraically closed field k is the zero-locus in the affine n-space $k^n$ of some finite family of polynomials of n variables with coefficients in k that generate a prime ideal. If the condition of generating a prime ideal is removed, such a set is called an (affine) algebraic set. A Zariski open subvariety of an affine variety is called a quasi-affine variety.

单词	Coordinate ring
释义	Coordinate ring 英语百科 Affine variety （重定向自Coordinate ring） In algebraic geometry, an affine variety over an algebraically closed field k is the zero-locus in the affine n-space $k^n$ of some finite family of polynomials of n variables with coefficients in k that generate a prime ideal. If the condition of generating a prime ideal is removed, such a set is called an (affine) algebraic set. A Zariski open subvariety of an affine variety is called a quasi-affine variety.
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