New answers tagged fields
2
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A version of Hilbert's Nullstellensatz for real zeros
The argument from the link that OP included can be mimicked: reducing the problem to complex Nullstellensatz with a bit of analysis. Consider a non-singlular point $\mathbf{p}\in Z$ near which the ...
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6
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Accepted
A version of Hilbert's Nullstellensatz for real zeros
I think, it does.
By change of coordinates, you may suppose that $Z$ contains the origin and the tangent vector space is the hyperplane $\{x_n=0\}$. Then, by implicit function theorem, for small ...
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32
votes
Accepted
Are the real numbers isomorphic to a nontrivial ultraproduct of fields?
The answer is no, because such ultrapowers are always $\aleph_1$-saturated, but $\mathbb{R}$ is not.
More concretely, the ultraproduct will be an ordered field with uncountable cofinality — every ...
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6
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Converse of "generalized Hilbert 90" / Galois descent
Let $R$ be a finite dimensional $L$-algebra with an action of ${\rm Gal}(L/K)$ such that $\sigma (\lambda .r)=\sigma (\lambda )\sigma (r)$, $\lambda\in L$, $r\in R$, $\sigma\in {\rm Gal}(L/K)$. Then ...
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