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is a limit of objects in the category of rings. But a limit of objects is always a product. And the product in the category of rings is just a
Cartesian product of rings. Is this actually correct? There's no citation. What are the restriction maps here?
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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.
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is the localisation map? This should correspond to repeatedly localising. which is what I intuitively would've expected.--
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712:{\displaystyle \Gamma \left(\bigcup _{i\in I}D_{fi},{\mathcal {O}}_{X}\right)=\operatorname {colim} _{i\in I}\phi _{i}}
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is? The article mentions that a vector space, equipped with a linear operator on it, can be viewed as a module over
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The technical term "represented" is not explained. The functor F is not represented by Spec(B), but by B.
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478:=0}. Then F is represented by Spec(B) where B is the quotient of K by the ideal I generated by the p
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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instead supposed to be something like "the polynomial ring mod out by the minimal polynomial of
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with respect to a preordered set that is not directed. I have edited the article accordingly.
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This kind of notation turns up in other places. For instance, it's analogous to the notation
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By the way, on
Knowledge talk pages it's conventional to write new comments at the bottom.
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A special but quite typical case of an affine scheme is obtained as follows. Take a
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This uses functors, but the article hasn't mentioned the functor connection yet.
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doesn't form a directed set. It's likely to be the colimit I described above.
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by B, as over the category of algebras it is covariant.
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A more useful example would describe Spec(B) in detail.
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