All Questions
4 questions
5
votes
1
answer
223
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Intrinsic characterisation of a class of rings
This may be well known, but I was unable to find an answer browsing literature. Let us temporarily call a commutative (unital) ring $R$ an O-ring if there exists an integer $n \ge 1$, a local field of ...
- 6,224
7
votes
1
answer
1k
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Given $v,w$ primes of $k$, is there $K/k$ so $K_v\cap\Bbb Q^\text{cycl}=K_w\cap\Bbb Q^\text{cycl}=K\cap\Bbb Q^\text{cycl}$?
For any field $k$, let $\mu(k)$ denote the roots of unity in $k$. Now let $k$ be a number field and let $v, w$ be non-archimedean primes of $k$ with distinct residual characteristics. Does there ...
- 2,799
1
vote
1
answer
325
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Maximal separable extension of $\mathbb F_q((t))$
Let $K=\mathbb F_q((t))$. I want to prove that $K^{sep}$ is composite of $K^{sep}(p)$ and $K^{sep}(not \ p)$, where $K^{sep}(p)$ is maximal Galois extension of $K$ of exponent $p$, $K^{sep}(not \ p)$ ...
- 11
2
votes
0
answers
124
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Property of a derivative in global field
Before posting I want to make it clear that I posted the same question in stack exchange awhile ago (https://math.stackexchange.com/questions/1533814/property-of-derivative-in-a-local-field) but didn'...
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