Talk:Spectrum of a ring
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I removed the following example:
- A special but quite typical case of an affine scheme is obtained as follows. Take a field K and n variables, x1,...,xn. Given m polynomials, p1,...,pm in these variables over K, there is a functor F from the category of commutative K-algebras to sets characterized by F(A)={(x1,...,xn) in An|p1=...=pm=0}. Then F is represented by Spec(B) where B is the quotient of K[x1,...,xn] by the ideal I generated by the pj.
Reasons:
- This uses functors, but the article hasn't mentioned the functor connection yet.
- The technical term "represented" is not explained. The functor F is not represented by Spec(B), but by B.
- A more useful example would describe Spec(B) in detail.
AxelBoldt 16:07, 18 Jan 2004 (UTC)
IMO, this article contains too much general rubbish. Just focus on the connections to geometry. Schemes are a generalisation of this setting and reside in a seperate article. agrosquid