Research Article

Central European Journal of Mathematics

, Volume 10, Issue 2, pp 824-834

K-quasiderivations

  • Caleb EmmonsAffiliated withDepartment of Mathematics, California State University - Los Angeles
  • , Mike KrebsAffiliated withDepartment of Mathematics, California State University - Los Angeles Email author 
  • , Anthony ShaheenAffiliated withDepartment of Mathematics, California State University - Los Angeles

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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-quasiderivation Polynomial ring Derivation system

MSC

13A99 08A40