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