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Results tagged with ac.commutative-algebra
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user 121225
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
11
votes
Does any derivation of commutative algebra preserve its nil-radical?
Here is another cute argument (I don't remember where I learned it, I think it is folklore). Let $P\subset A$ be an arbitrary prime ideal. We claim it contains a $D$-stable prime ideal. For this, cons …
- 374
4
votes
Accepted
Etale map has image whose complement is the vanishing locus of a finitely generated ideal
Let $U$ be the image of $\operatorname{Spec} B$ in $\operatorname{Spec} A$. Since the map $\operatorname{Spec} B \to \operatorname{Spec} A$ is open, $U$ is open. And since $\operatorname{Spec} B$ is q …
- 374