RT info:eu-repo/semantics/article
T1 General remainder theorem and factor theorem for polynomials over non-commutative coefficient rings
A1 Cuida Gómez, María Astrid
A1 Laudano, Francesco
A1 Martínez Moro, Edgar
K1 Remainder theorem
K1 Factor theorem
K1 Long division
K1 Left modulo-m congruence
K1 Polynomial divisibility criterion
K1 Non-commutative coefficient ring
K1 12
AB 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.
PB Taylor & Francis
SN 0020-739X
YR 2020
FD 2020
LK https://uvadoc.uva.es/handle/10324/78208
UL https://uvadoc.uva.es/handle/10324/78208
LA eng
NO International Journal of Mathematical Education in Science and Technology, 2020, v. 51, n. 5, p. 775-785
NO Producción Científica
DS UVaDOC
RD 16-oct-2025