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Master's Dissertation
DOI
10.11606/D.55.2008.tde-21052008-150202
Document
Author
Full name
Thiago Castilho de Mello
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2008
Supervisor
Committee
Dias, Ires (President)
Koshlukov, Plamen Emilov
Milies, Francisco Cesar Polcino
Title in Portuguese
Sobre bases normais para extensões galoisianas de corpos
Keywords in Portuguese
Base normal generalizada
Bases normal
Construção de bases normais
Elemento normal
Elemento primitivo
Extensões abelianas
Extensões cíclicas
Forma hermitiana
Forma traço
Teoria de Galois
Abstract in Portuguese
Neste trabalho apresentamos várias demonstrações do Teorema da Base Normal para certos tipos de extensões galoisianas de corpos, algumas existenciais e outras construtivas, destacando as diferenças e dificuldades de cada situação. Apresentamos também generalizações de tal teorema e mostramos que toda extensão galoisiana de grau ímpar de corpos admite uma base normal autodual com respeito µa forma bilinear traço
Title in English
On normal bases for galoisian extensions of fields
Keywords in English
Abelian extension
Construction of normal bases
Cyclic extension
Galois theory
Generalized normal base
Hermitian form
Normal base
Normal element
Primitive element
Trace map
Abstract in English
In this work we present several demonstrations of The Normal Basis Theorem for certain kinds of galoisian extensions of fields, some of them existential and others constructive, pointing the diffculties and differences in each situation. We also present generalizations of such theorem and show that every odd degree galoisian extension of fields admits a self-dual normal base with respect to the trace bilinear map
 
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thiago.pdf (433.20 Kbytes)
Publishing Date
2008-05-26
 
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