| 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. |
