Central European Journal of Mathematics

, Volume 10, Issue 2, pp 824–834

K-quasiderivations

Research Article

DOI: 10.2478/s11533-011-0140-x

Cite this article as:
Emmons, C., Krebs, M. & Shaheen, A. centr.eur.j.math. (2012) 10: 824. doi:10.2478/s11533-011-0140-x
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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.

Keywords

K-quasiderivationPolynomial ringDerivation system

MSC

13A9908A40

Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2011

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia State University - Los AngelesLos AngelesUSA