# Hagen

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|           |                  | bio     | visits   |            |                   |
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|           | 3,347 reputation | website |          | member for | 2 years, 7 months |
| 49 badges | location         |         | seen     | yesterday  |                   |

# 221 Actions

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| May15 | comment  | Non-isomorphic simple extensions of the same degree of a field of positive characteristicYour approach will not work, because over the finite field $F_p$ (I assume you mean the field with $p$ elements) all irreducible polynomials are separable. However if you replace $F_p$ with a non-perfect field, then this works. It then remains to treat the case of a separably closed field $K$, that is a field that possesses only purely inseparable extensions ... |
| May8  | answered | Integral closure $\tilde{A}$ is flat over $A$, then $A$ is integrally closed                                                                                                                                                                                                                                                                                                                                                                                          |
| May2  | answered | Linear Transformations: Scaling along the line $y=x$                                                                                                                                                                                                                                                                                                                                                                                                                  |
| Apr30 | revised  | every field of characteristic 0 has a discrete valuation ring?added 1 characters in body                                                                                                                                                                                                                                                                                                                                                                              |
| Apr30 | comment  | every field of characteristic 0 has a discrete valuation ring?The answer to your question is "No". The reals do not carry discrete valuations for almost the same reason as for the complex numbers: one can take $n$-th roots of positve elements for every $n\in\mathbb{N}$.                                                                                                                                                                                        |
| Apr29 | revised  | every field of characteristic 0 has a discrete valuation ring?added 552 characters in body                                                                                                                                                                                                                                                                                                                                                                            |
| Apr29 | comment  | every field of characteristic 0 has a discrete valuation ring?I do not agree with your statement: every field $K$ has a proper subdomain $R$ such that $K$ is the fraction field of $R$. Take a transcendence basis $T$ of $K$ over the prime field $P$ and consider the integral closure $R$ of the polynomial ring $P[T]$ in $K$.                                                                                                                                   |
| Apr29 | comment  | $\mathbb A^n(k)$ and $\mathbb A^n(k)\setminus \{0\}$ are not homeomorphic                                                                                                                                                                                                                                                                                                                                                                                             |
| Apr28 | revised  | every field of characteristic 0 has a discrete valuation ring?added 832 characters in body                                                                                                                                                                                                                                                                                                                                                                            |
| Apr28 | comment  | every field of characteristic 0 has a discrete valuation ring?In my answer I was assuming that the DVR has fraction field equal to $\mathbb{C}$. Otherwise the statement has a trivial proof because every field of characteristic $0$ contains the rationals.                                                                                                                                                                                                        |
| Apr27 | answered | every field of characteristic 0 has a discrete valuation ring?                                                                                                                                                                                                                                                                                                                                                                                                        |
| Apr18 | comment  | Does every algebraically closed field contain the field of complex numbers?The cardinality of a transcendence basis of $\mathbb{C}/\mathbb{Q}$ equals the cardinality of $\mathbb{R}$.                                                                                                                                                                                                                                                                                |
| Apr18 | answered | Does every algebraically closed field contain the field of complex numbers?                                                                                                                                                                                                                                                                                                                                                                                           |
| Apr16 | answered | Valuation but not Noetherian Rings                                                                                                                                                                                                                                                                                                                                                                                                                                    |
| Apr16 | answered | Value range of normalization methods? min-max, z-score, decimal scaling                                                                                                                                                                                                                                                                                                                                                                                               |
| Apr15 | comment  | The field of Laurent series over $\mathbb{C}$ is quasi-finiteI see how one can avoid general theory at various points. In particular one can specialize the proof for the fact that the Galois group is cyclic to the present particular case. However in this way one will arrive at a rather lengthy verification. And at the moment I don't see how to avoid using something like Hensel's lemma at the beginning of the whole argument ...                        |
| Apr15 | answered | The field of Laurent series over $\mathbb{C}$ is quasi-finite                                                                                                                                                                                                                                                                                                                                                                                                         |
| Apr12 | answered | Non-trivial valuation of $\mathbb R$                                                                                                                                                                                                                                                                                                                                                                                                                                  |
| Apr10 | awarded  | Custodian                                                                                                                                                                                                                                                                                                                                                                                                                                                             |
| Apr10 | reviewed | Reject suggested edit on Isomorphism or non-isomorphism of two specific local rings                                                                                                                                                                                                                                                                                                                                                                                   |
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