On Ritt's decomposition theorem in the case of finite fields

Authors:
Jaime Gutierrez;David Sevilla
Affiliations:
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, E-39071 Santander, Spain;Department of Computer Science, Concordia University, 1455 de Maisonneuve W., Montreal, Canada H3G 1M8
Venue:
Finite Fields and Their Applications
Year:
2006

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Abstract

A classical theorem by Ritt states that all the complete decomposition chains of a univariate polynomial satisfying a certain tameness condition have the same length. In this paper we present our conclusions about the generalization of these theorem in the case of finite coefficient fields when the tameness condition is dropped.