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

• A. Cuida ^[1] ; F. Laudano ^[2] ; E. Martinez-Moro ^[1]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
  2. [2] University of Salerno

     University of Salerno

     Fisciano, Italia

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 51, Nº. 5, 2020, págs. 775-785
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative).

    These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. Finally, we will refer to some applications of these results for evaluating and dividing on skew polynomial rings. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities.