Timeline for Completing vs Extending a field
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 2, 2017 at 0:33 | history | edited | Todd Trimble |
completeness tag removed per meta discussion
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| Apr 20, 2017 at 23:20 | comment | added | Gerry Myerson | What metric are you applying, Shake, to decide which of two strategies is the better one? | |
| Apr 20, 2017 at 20:51 | comment | added | Emil Jeřábek | The completion of an algebraically closed valued field is algebraically closed. So, for any valued field, just two steps are enough: first take algebraic closure, then take completion. | |
| Apr 20, 2017 at 16:48 | comment | added | js21 | For $p$-adic numbers, one can do it with a single completion : first choose an algebraic closure $\bar{\mathbb{Q}}$, let $\bar{\mathbb{Z}}$ be the integral closure of $\mathbb{Z}$ in it, consider $A$ the $p$-adic completion of the local ring of $\bar{\mathbb{Z}}$ at some (chosen) maximal ideal above $p$, and finally let $\Omega = A [ \frac{1}{p}]$. | |
| Apr 20, 2017 at 16:07 | history | asked | Shake Baby | CC BY-SA 3.0 |