# K-quasiderivations

Caleb Emmons; Mike Krebs; Anthony Shaheen

Open Mathematics (2012)

- Volume: 10, Issue: 2, page 824-834
- ISSN: 2391-5455

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topCaleb Emmons, Mike Krebs, and Anthony Shaheen. "K-quasiderivations." Open Mathematics 10.2 (2012): 824-834. <http://eudml.org/doc/269700>.

@article{CalebEmmons2012,

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.},

author = {Caleb Emmons, Mike Krebs, Anthony Shaheen},

journal = {Open Mathematics},

keywords = {K-quasiderivation; Polynomial ring; Derivation system},

language = {eng},

number = {2},

pages = {824-834},

title = {K-quasiderivations},

url = {http://eudml.org/doc/269700},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Caleb Emmons

AU - Mike Krebs

AU - Anthony Shaheen

TI - K-quasiderivations

JO - Open Mathematics

PY - 2012

VL - 10

IS - 2

SP - 824

EP - 834

AB - 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.

LA - eng

KW - K-quasiderivation; Polynomial ring; Derivation system

UR - http://eudml.org/doc/269700

ER -

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