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Master's Dissertation
DOI
Document
Author
Full name
Bruno Leonardo Macedo Ferreira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Guzzo Junior, Henrique (President)
Ferreira, Joao Carlos da Motta
Peresi, Luiz Antonio
Title in Portuguese
Álgebras train
Keywords in Portuguese
Álgebras
Álgebras train
Train
Abstract in Portuguese
Estudamos a estrutura de álgebras de potências associativas que são álgebras train. Primeiramente, mostramos a existência de idempotentes, que são todos principais e absolutamente primitivos. Em seguida, vemos as equações train envolvendo a decom- posição de Peirce. Quando a álgebra é de dimensão finita, resulta que a dimensão das componentes de Peirce são invariantes e o limite superior para seus nilndices são es- tudados para alguns idempotentes. Além disso, mostramos que as álgebras localmente train são álgebras train. Damos então uma descrição completa para o conjunto dos idempotentes para obter suas fórmulas explcitas. É voltada uma atenção para o caso de álgebras de Jordan, onde discutimos condições para que álgebras train de potências as- sociativas sejam álgebras de Jordan. Também mostramos que álgebras train de Jordan são de dimensão finita. Para álgebras de Bernstein de ordem n e perodo p, provamos que para termos associatividade nas potências necessitamos p = 1. Neste caso, existem 2 n1 possibilidades de equações train, que são explicitamente descritas.
Title in English
Train Algebras
Keywords in English
Algebras
Algebras train
Train
Abstract in English
We study the structure of power associative algebras which are train algebras. First we show the existence of idempotents, which are all principal and absolutely primitive. Then consider the train equations involving the Peirce decomposition. When the alge- bra is finite dimensional, it follows that the size of the Pierce components are invariant and the upper limit for its nil-indexes are studied for some idempotent. Furthermore, we show that locally train algebras are train algebras. Then we get a complete de- scription for the set of idempotents to obtain their explicit formulas. We give attention to the case of Jordan algebras, where we discuss conditions for train power associa- tive algebras be Jordan algebras. We also show that Jordan train algebras are finite dimensional. For Bernstein algebras of order n and period p, we prove that to have associativity in the powers we need p = 1. In this case, there are 2 n1 possibilities of train equations, which are explicitly described.
 
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Publishing Date
2019-09-23
 
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