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2012 | 10 | 2 | 824-834
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K-quasiderivations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
2
Strony
824-834
Opis fizyczny
Daty
wydano
2012-04-01
online
2012-01-18
Twórcy
autor
  • California State University - Los Angeles
autor
Bibliografia
  • [1] Adler I., Composition rings, Duke Math. J., 1962, 29(4), 607–623 http://dx.doi.org/10.1215/S0012-7094-62-02961-7
  • [2] Barbeau E.J., Remarks on an arithmetic derivative, Canad. Math. Bull., 1961, 4, 117–122 http://dx.doi.org/10.4153/CMB-1961-013-0
  • [3] Emmons C., Krebs M., Shaheen A., How to differentiate an integer modulo n, College Math. J., 2009, 40(5), 345–353 http://dx.doi.org/10.4169/074683409X475661
  • [4] Fechter T., Exploring the Derivative of a Natural Number Using the Logarithmic Derivative, Senior Capstone thesis, Pacific University, 2007
  • [5] Gleason A.M., Greenwood R.E., Kelly L.M. (Eds.), The William Lowell Putnam Mathematical Competition. Problems and Solutions: 1938–1964, Mathematical Association of America, Washington, 1980
  • [6] Kautschitsch H., Müller W.B., Über die Kettenregel in A [x 1,...x n], A (x 1...x n) und A [[x 1,...x n]], In: Contributions to General Algebra, 1, Klagenfurt, May 25–28, 1978, Johannes Heyn, Klagenfurt, 1979, 131–136
  • [7] Lausch H., Nöbauer W., Algebra of Polynomials, North-Holland Math. Library, 5, North-Holland, Amsterdam-London, 1973
  • [8] Menger K., General algebra of analysis, Reports of Mathematical Colloquium, 1946, 7, 46–60
  • [9] Müller W., Eindeutige Abbildungen mit Summen-, Produkt- und Kettenregel im Polynomring, Monatsh. Math., 1969, 73(4), 354–367 http://dx.doi.org/10.1007/BF01298986
  • [10] Müller W.B., The algebra of derivations, An. Acad. Brasil. Ciênc., 1973, 45, 339–343 (in Spanish)
  • [11] Müller W.B., Differentiations-Kompositionsringe, Acta Sci. Math. (Szeged), 1978, 40(1–2), 157–161
  • [12] Müller W.B., Über die Kettenregel in Fastringen, Abh. Math. Sem. Univ. Hamburg, 1979, 48(1), 108–111 http://dx.doi.org/10.1007/BF02941293
  • [13] Nöbauer W., Derivationssysteme mit Kettenregel, Monatsh. Math., 1963, 67(1), 36–49 http://dx.doi.org/10.1007/BF01300680
  • [14] Stay M., Generalized number derivatives, J. Integer Seq., 2005, 8(1), #05.1.4
  • [15] Ufnarovski V., Ahlander B., How to differentiate a number, J. Integer Seq., 2003, 6(3), #03.3.4
  • [16] Westrick L., Investigations of the number derivative, preprint available at http://www.plouffe.fr/simon/OEIS/archive_in_pdf/intmain.pdf
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0140-x
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