Re: [math-fun] Continuous derivations on the reals
Ki Song wrote: << I thought 'derivation' was restricted to linear operators. Perhaps these operators should be called something like quasi-derivation, or pseudo-derivation?
Derivations are defined for rings, fields, and algebras. Cf. http://en.wikipedia.org/wiki/Derivation_%28abstract_algebra%29 . --Dan
On 6/18/07, Dan Asimov <dasimov@earthlink.net> wrote:
Derivations are defined for rings, fields, and algebras. Cf. http://en.wikipedia.org/wiki/Derivation_%28abstract_algebra%29 .
--Dan
There's also the concept of a number derivative: { 0 if k = 0 or 1 k' = { 1 if k prime { p' q + p q' if k = p q http://en.wikipedia.org/wiki/Number_derivative I extended the idea to finite fields here: http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Stay/stay44.html -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
Dan Asimov <dasimov@earthlink.net> wrote:
Ki Song wrote:
I thought 'derivation' was restricted to linear operators. Perhaps these operators should be called something like quasi-derivation, or pseudo-derivation?
Derivations are defined for rings, fields, and algebras. Cf. http://en.wikipedia.org/wiki/Derivation_%28abstract_algebra%29
The wikipedia article is wrong. As Ki and I have stressed, ring derivations are defined as Z-linear Leibniz operators. This definition has been the universal standard for at least 75 years if not longer. One should choose another name for *nonlinear* Leibniz operators. If you search mathematical publications via Google scholar/books or Amazon books you will find ample confirmation of these statements. Beware that the quality of wikipedia math articles varies widely. --Bill Dubuque
participants (3)
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Bill Dubuque -
Dan Asimov -
Mike Stay