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Doctoral Thesis
DOI
Document
Author
Full name
Bruno Leonardo Macedo Ferreira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Guzzo Junior, Henrique (President)
Arenas, Manuel
Costa, Roberto Celso Fabricio
Murakami, Lucia Satie Ikemoto
Silva, Juaci Picanço da
Title in Portuguese
Aditividade de aplicações e b-decomposição de Wedderburn
Keywords in Portuguese
Aplicações
Decomposição
Wedderburn
Abstract in Portuguese
A tese está dividida em duas partes. A primeira parte é dedicada a análise de quando certas aplicações definidas em uma classe de anéis não-associativos são aditivas. Esta questão foi estudada para anéis associativos por Martindale, [38], e outros, [35], [4], [22], [23], [37], [39], [36], [7] e [27]. Para anéis de Jordan, foi estudada por Ji Peisheng, [26], e para anéis alternativos por Ferreira e Guzzo, [12], [13] e [14]. Muito pouco se conhece ainda sobre esta questão com relação a anéis e álgebras não-associativas em geral. Assim, um propósito é o de tentar ampliar ou aprofundar esse conhecimento para outras classes de anéis não-associativos. Um teorema muito importante na teoria das álgebras associativas é o Teorema de Wedderburn. A segunda parte a ser investigada nesta tese procura provar um teorema do tipo Wedderburn para b-álgebras do tipo (, ). Muitos autores buscam provar um teorema do tipo de Wedderburn para algumas álgebras não-associativas, já temos isso feito para as álgebras alternativas e de Jordan. No caso das b-álgebras definimos: No capitulo 4, definimos bdecomposição de Wedderburn. Assim, outra linha es- tudada é ver se alguma b-álgebra possu uma b-decomposição de Wedderburn.
Title in English
Application additivity and b-decomposition of Wedderburn
Keywords in English
Analysis
Applications
Wedderburn
Abstract in English
The thesis is divided into two parts. The first part is dedicated to analysis when certain applications defined in a class of non-associative rings are additive. This question was studied for associative rings by Martindale, [38], and others, [35], [4], [22], [23], [37] , [39], [36], [7] and [27]. For Jordans rings, it was studied by Ji Peisheng, [26], and for alternative rings, by Ferreira and Guzzo, [12], [13] and [14]. We know very few results with regard to nonassociative rings and algebras, in general. This way, a purpose is the one of try to extend or to deepen that knowledge to other classes of non-associative rings. A very important theorem in the theory of associative algebras is the Theorem of Wedderburn. The second part to be investigated try to prove a theorem of Wedderburn type to b-algebras (, ) type. Many authors seek to prove a theorem of Wedderburn for some type of non-associative algebras, we have done it for alternative algebras and Jordan. In the case of b-algebras defined: In chapter 4, we define bWedderburn decomposition. Thus, another line study is to see if some b-algebra possess a b-Wedderburn decomposition.
 
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Publishing Date
2019-09-25
 
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