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Results tagged with fields
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user 17907
Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].
14
votes
Accepted
Why does inconstructibility of $\sqrt[3]{2}$ imply impossibility of cube doubling?
Disclaimer: The following perhaps isn't an answer to your question as stated, so my apologies if this answer is useless to you. However, you're asking for how to treat this problem "honestly", and I t …
- 4,746
8
votes
Obstructions for a group to be the multiplicative group of a field
Restricting to $\mathbb{Q}$-rank zero, there are more complicated torsion examples, such as $G=\mathbb{Z}[1/5]/\mathbb{Z}$. If $K^\times=G$, then $K$ must be algebraic over a finite field $k=\mathbb{F …
- 4,746
3
votes
Accepted
What is the state-of-the-art for solving polynomials systems over fields that are not algebr...
For the reals, I particularly like the book by Sturmfels mentioned by Alexandre Eremenko. For the rational numbers, you can hardly do better than Bjorn Poonen's book Rational Points on Varieties, whic …
- 4,746
1
vote
How to show an invariant subfield of rational function field $\mathbb{Q}(x)$ under a certain...
The answer as to the surjectivity of $\alpha$ is no. As in algebraic number theory, the simplest way to prove that an element is not a norm is by local considerations. Let us consider
$$
y=\frac{(x^3- …