Solving quadratic equations over polynomial rings of characteristic two.

Título inglés Solving quadratic equations over polynomial rings of characteristic two.
Título español Resolución de ecuaciones cuadráticas sobre anillos polinómicos de característica dos.
Autor/es Cherly, Jorgen ; Gallardo, Luis ; Vaserstein, Leonid ; Wheland, Ethel
Organización Dep. Math. Univ. Brest, Brest, Francia;Dep. Math. Penn State Univ., University Park (Pennsylvania), Estados Unidos;Dep. Math. Univ. Akron, Akron (Ohio), Estados Unidos
Revista 0214-1493
Publicación 1998, 42 (1): 131-142, 11 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.
We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1, ..., xN) for any finite field F and any number N of variables.
The case of quadratic equations in characteristic two is studied in detail.
Clasificación UNESCO 120113
Palabras clave español Ecuaciones polinómicas ; Anillos de polinomios ; Grupos finitos
Código MathReviews MR1628154
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