Timeline for Generalization of a field norm to the linear group
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2018 at 19:06 | review | Close votes | |||
| Mar 7, 2018 at 2:49 | |||||
| Mar 6, 2018 at 18:27 | comment | added | LSpice | Probably too complicated, but: there is no harm in passing to the purely inseparable closures of $k$ and $K$. After doing so, we may replace $x$ by its semisimple part (which now must be $K$-rational) without changing either side. By induction on the dimension of $V$, it suffices to assume that $V$ contains no proper, non-$0$, $x$-stable subspace. Then any choice of non-$0$ element of $V$ furnishes a $K[x]$-linear isomorphism $V \cong E$, where $E$ is the extension obtained by adjoining to $K$ a root of the minimal polynomial of $x$. Then your equality is transitivity of the norm. | |
| Mar 6, 2018 at 18:23 | answer | added | S. carmeli | timeline score: 2 | |
| Mar 6, 2018 at 17:55 | history | asked | Jesua Israel Epequin Chavez | CC BY-SA 3.0 |