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K-quasiderivations

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Emmons C., Krebs M., Shaheen A.

Open Mathematics

2012

tom 10

nr 2

824-834

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.

Ograniczanie wyników

1 Open Mathematics

1 Emmons C.

1 Krebs M.

1 Shaheen A.

1 2012

Wyniki wyszukiwania

K-quasiderivations