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Classroom Notes

General remainder theorem and factor theorem for polynomials over non-commutative coefficient rings

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Pages 775-785 | Received 24 Apr 2019, Published online: 20 Oct 2019

References

  • Blitzer R. (2014). Precalculus (5th ed.). Miami: Pearson.
  • Caruso X., & Le Borgne J. (2012). Some algorithms for skew polynomials over finite fields. Preprint, arXiv:1212.3582.
  • Cajori F. (1911). Horner's method of approximation anticipated by Ruffini. Bulletin of the American Mathematical Society, 17(8), 409–414. doi: 10.1090/S0002-9904-1911-02072-9
  • Cox D. A., Little J., & O'Shea D. (2015). Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra (4th ed.). Undergraduate Texts in Mathematics. Cham: Springer.
  • Dobbs D. E. (2007). The remainder theorem and factor theorem for polynomials over noncommutative coefficient rings. International Journal of Mathematical Education in Science and Technology, 38(2), 268–273. doi:10.1080/00207390600913350
  • Erić A. Lj. (2008). The resultant of non-commutative polynomials. Matematicki Vesnik, 60(1), 3–8.
  • Jacobson N. (1996). Finite dimensional division algebras over fields. New York, NY: Springer.
  • Joseph G. (2011). The crest of the peacock: Non-European roots of mathematics. Princeton, NJ: Princeton University Press.
  • Lagrange J. L. (1826). Traité de la résolution des équations numériques de tous les degrés: avec des notes sur plusieurs points de la théorie des équations algébriques (p. 126). Paris: Bachelier.
  • Lam T. Y., & Leroy A. (1988). Vandermonde and Wronskian Matrices over Division Rings. Journal of Algebra, 119, 308–336. doi: 10.1016/0021-8693(88)90063-4
  • Lang S. (2002). Algebra (3rd ed.). New York, NY: Springer-Verlag.
  • Laudano F. (2018). A generalization of the remainder theorem and factor theorem. IJMEST. doi:10.1080/0020739X.2018.1522676
  • Ling W., & Needham J. (1954). Horner's method in Chinese mathematics: Its origins in the root-extraction procedures of the Han dynasty. T'oung Pao -+ International Journal of Chinese Studies, 43(1), 345–401. doi:10.1163/156853254X00146
  • Mac Lane S., & Birkhoff G. (1985). Algebra. Milano: Mursia.
  • Martínez-Penas U. (2018). Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring. Journal of Algebra, 504, 587–612. doi:10.1016/j.jalgebra.2018.02.005
  • McAskill B., Watt W., Balzarini E., Johnson B., Kennedy R., Melnyk T., & Zarski C. (2012). Pre-calculus 12. New York, NY: McGraw-Hill Ryerson.
  • Montucla J. (1800). Histoire des mathématiques (Vol. 2, 3:3, pp. 601–603). Paris.
  • Rotman J. J. (2003). Advanced modern algebra. New York, NY: Prentice-Hall.
  • Smits T. H. M. (1968). Skew polynomial rings. Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae (Vol. 71). doi:10.1016/S1385-7258(68)50022-2.
  • Smoryski C. (2007). History of mathematics: A supplement. New York: Springer Science & Business Media.
  • Wimmer H. K. (1990, January). On the history of the Bezoutian and the resultant matrix. Linear Algebra and its Applications, 128, 27–34. doi: 10.1016/0024-3795(90)90280-P

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