Abstract
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.
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Emmons, C., Krebs, M. & Shaheen, A. K-quasiderivations. centr.eur.j.math. 10, 824–834 (2012). https://doi.org/10.2478/s11533-011-0140-x
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DOI: https://doi.org/10.2478/s11533-011-0140-x