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Doctoral Thesis
DOI
10.11606/T.45.2007.tde-04122007-134732
Document
Author
Full name
Érica Zancanella Fornaroli
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Ferreira, Vitor de Oliveira (President)
Ferrero, Miguel Angel Alberto
Goncalves, Jairo Zacarias
Kochloukov, Plamen Emilov
Tengan, Eduardo
Title in Portuguese
Corpos livres em anéis com divisão
Keywords in Portuguese
anel
anel com divisão
corpo livre
valorização.
Abstract in Portuguese
Sejam $D$ um anel com divisão, $K$ um subanel com divisão de $D$ e $X$ um conjunto. O $D$-anel livre sobre $K$ em $X$, $D_K\langle X angle=D\underset{\ast} K \langle X angle$, possui um corpo universal de frações denominado corpo livre e denotado por $D_K\X$. Neste trabalho fazemos uma investigação acerca de condições que, quando satisfeitas por um anel com divisão, sejam suficientes para garantir a existência de um subanel isomorfo a algum corpo livre não-comutativo, e também descrevemos famílias de anéis com divisão que satisfazem as condições encontradas. Os anéis com divisão que provamos conter um corpo livre são, em sua maioria, completamentos de corpos de frações de domínios noetherianos com topologia definida por uma valorização.
Title in English
Free fields in division rings
Keywords in English
division ring
free field
ring
valuation.
Abstract in English
Let $D$ be a division ring, $K$ a subfield of $D$ and $X$ a set. The $D$-free ring over $K$ on $X$, $D_K\langle X angle=D\underset{\ast} K\langle X angle$, has an universal field of fractions called a free field and denoted by $D_K\X$. In this work we look into conditions which, when satisfied by a division ring, are sufficient to guarantee the existence of a subring isomorphic to some non-commutative free field, and we also describe families of division rings which satisfy the conditions that were found. The majority of the division rings that we proved to contain a free field are completions of fields of fractions of Noetherian domains with topology defined by a valuation.
 
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tesecorrigida.pdf (568.18 Kbytes)
Publishing Date
2012-04-12
 
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