Noncommutative polynomial maps

André Leroy (1)

1 LML - Laboratoire de Mathématiques de Lens

Polynomial maps attached to polynomials of an Ore extension are naturally defi ned. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a fi nite fi eld F_q[t;S ], where S is the Frobenius automorphism, are translated into factorizations in the usual polynomial ring F_q[x].

Mots clés: Polynomial maps; pseudo-linear transformations; Skew polynomial rings

Domaines: Anneaux et algèbres [math.RA]

André Leroy. Noncommutative polynomial maps. 2012. ⟨hal-00722231⟩