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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2020.tde-08022021-141849
Document
Author
Full name
Carlos André Gomes Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Rodrigues, Rodrigo Lucas (President)
Hernandez, Ma Isabel
Solís, Victor Hugo López
Title in Portuguese
Comprimentos de álgebras não associativas
Keywords in Portuguese
Álgebra
Cadeia
Comprimento
Conjunto gerador
Dimensão
Palavra irredutível
Abstract in Portuguese
Nesta dissertação estudamos o comprimento de álgebras de dimensão finita. Estabelecemos limites superiores para seus comprimentos e exibimos propriedades construtivas dos conjuntos geradores para álgebras arbitrárias em dimensões inferiores a 5. Além disso, fornecemos uma classificação das álgebras alternativas de dimensão inferior a 6 sobre corpos perfeitos baseada em seus comprimentos.
Title in English
Lengths of non-associative algebras
Keywords in English
Algebra
Chain
Dimension
Generating set
Irreducible word
Length
Abstract in English
In this work we study the length of finite-dimensional algebras. We establish upper bounds to their lengths and exhibit constructive properties of generating sets for arbitrary algebras of dimension smaller than 5. Furthermore a complete classification up to isomorphism is given to alternative algebras of dimension smaller than 6 over perfect fields based on its length.
 
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CompAlg_Carlos.pdf (536.52 Kbytes)
Publishing Date
2021-07-06
 
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