A K-quasiderivation is a map which satisfies both the Product Rule and the Chain Rule. In this paper, we discuss several interesting families of K-quasiderivations. We first classify all K-quasiderivations on the ring of polynomials in one variable over an arbitrary commutative ring R with unity, thereby extending a previous result. In particular, we show that any such K-quasiderivation must be linear over R. We then discuss two previously undiscovered collections of (mostly) nonlinear K-quasiderivations on the set of functions defined on some subset of a field. Over the reals, our constructions yield a one-parameter family of K-quasiderivations which includes the ordinary derivative as a special case.
@article{bwmeta1.element.doi-10_2478_s11533-011-0140-x,
author = {Caleb Emmons and Mike Krebs and Anthony Shaheen},
title = {K-quasiderivations},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {824-834},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0140-x}
}
Caleb Emmons; Mike Krebs; Anthony Shaheen. K-quasiderivations. Open Mathematics, Tome 10 (2012) pp. 824-834. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0140-x/
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