Re: What is a "differential field"?

From: Michael Barr (barr_at_barrs.org)
Date: 08/12/04 

Date: 12 Aug 2004 16:27:28 -0700

"Norm Dresner" <ndrez@att.net> wrote in message news:<ULOSc.435795$Gx4.204175@bgtnsc04-news.ops.worldnet.att.net>...
> Wikipedia doesn't have a definition and Mathworld has too many hits but no
> definition, just articles in which the two words occurred. I tried quoting
> the phrase and gont something that wasn't a definition either.
>
> A real definition or URL would be helpful.
>
> A secondary question: What exactly is Galois theory for DF's?
>
> Thanks
> Norm

Don't know too much about it, but it is a field equipped with a
derivation: an additive map d:F --> F such that d(xy) = x.dy + y.dx
(sometimes called the Leibniz formula).

I would have to guess that a Galois theory is a way of associating a
group (or maybe a Lie algebra) to an extension of one in such a way
that subgroups correspond to intermediate extensions.

I might point out that Sophus Lie created (what we call) Lie groups in
order to do for differential equations what Galois theory did for
polynomial equations. Of course, Lie theory is much harder than
Galois theory.

Relevant Pages

  • Re: JSH-Really on a roll today
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  • Re: What is a "differential field"?
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  • Re: Field Extension Question
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