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Message from discussion f split => f' split
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David Madore  
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 More options Mar 28 2005, 9:00 pm
Newsgroups: sci.math.research
From: david.mad...@ens.fr (David Madore)
Date: Tue, 29 Mar 2005 02:00:12 +0000 (UTC)
Local: Mon, Mar 28 2005 9:00 pm
Subject: f split => f' split
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Can anything interesting be said about a field K such that, for any
polynomial f over K which is split (all its root are in K), f' is also
split?  Does this property have a name?

If K is real-closed, it is easy to see that it satisfies the property.
I'm not sure I can come up with any other example, in fact.

What about the smallest subfield of the algebraic closure of the
rationals which satisfies the property in question (it is clear that
it exists)?  What does it "look like"?

--
     David A. Madore
    (david.mad...@ens.fr,
     http://www.dma.ens.fr/~madore/ )


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