Timeline for Is the minimal polynomial of an algebraic formal Laurent series always separable?

Current License: CC BY-SA 4.0

18 events

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Apr 25, 2022 at 14:34	comment	added	François Brunault		One may argue using the following separability criterion (maybe it boils down to the same computations): $K(x)(f)/K(x)$ is separable if and only if $A := K(x)(f) \otimes_{K(x)} K(x)^{1/p}$ is reduced. We have $K(x)^{1/p}=K^{1/p}(x^{1/p})$ so that $A \hookrightarrow K((x)) \otimes_{K(x)} K^{1/p}(x^{1/p}) \hookrightarrow K^{1/p}((x^{1/p}))$.
Apr 25, 2022 at 13:59	history	edited	reuns	CC BY-SA 4.0	added 2 characters in body
Apr 25, 2022 at 11:13	vote	accept	Jiu
Apr 24, 2022 at 3:30	comment	added	reuns		If $f'\ne 0$ then $\gcd(f,f')$ divides $f$
Apr 24, 2022 at 3:19	comment	added	Jiu		And why is $f(y)=g(y^p)$?
Apr 24, 2022 at 2:03	history	edited	reuns	CC BY-SA 4.0	added 4 characters in body
Apr 24, 2022 at 1:59	comment	added	reuns		@Jiu $\{ a\in \overline{K},\exists n, a^{p^n}\in K\}$ which is a field in characteristic $p$. But in my answer you can replace it by $\overline{K}$ it works the same way.
Apr 24, 2022 at 1:09	comment	added	Jiu		Thank you for the answer! Could you tell me what is $K^{1/p^\infty}$?
Apr 23, 2022 at 21:26	history	edited	reuns	CC BY-SA 4.0	added 8 characters in body
Apr 23, 2022 at 19:11	history	edited	reuns	CC BY-SA 4.0	added 16 characters in body
Apr 23, 2022 at 19:05	history	edited	reuns	CC BY-SA 4.0	added 16 characters in body
Apr 23, 2022 at 19:02	history	undeleted	reuns
Apr 23, 2022 at 19:00	history	edited	reuns	CC BY-SA 4.0	added 434 characters in body
Apr 23, 2022 at 18:55	history	edited	reuns	CC BY-SA 4.0	added 434 characters in body
Apr 23, 2022 at 13:07	history	deleted	reuns		via Vote
Apr 23, 2022 at 13:05	history	edited	reuns	CC BY-SA 4.0	added 6 characters in body
Apr 23, 2022 at 13:00	history	edited	reuns	CC BY-SA 4.0	edited body
Apr 23, 2022 at 12:54	history	answered	reuns	CC BY-SA 4.0

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