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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.1999.tde-20210729-022421
Document
Author
Full name
Sidnei Azevedo de Souza
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1999
Supervisor
Title in Portuguese
O problema de Specht em álgebras de Bernstein
Keywords in Portuguese
Álgebra
Abstract in Portuguese
Este trabalho resultou do estudo do artigo Polynomial identities of Bernstein algebras of small dimension de J. Bernard, S.González, G. Martinez e A.V.Iltyakov, publicado no J.Algebra em 1998. Consideramos o problema de Specht, isto é, o problemada existência de uma base finita de identidades (polinomiais), para as álgebras de Bernstein. No Capítulo I, mencionamos que este problema não tem solução para as álgebras de Bernstein, tem solução para as álgebras de Bernstein-Jordan e para asálgebras de Bernstein nucleares, e mostramos que o ideal de identidades de uma álgebra de Bernstein particular de dimensão 2 tem um conjunto finito de geradores. No Capítulo 2, encontramos um conjunto finito de identidades que gera o ideal deidentidades da classe formada pelas álgebras de Bernstein regulares. No Capítulo 3, encontramos um conjunto finito de identidades que gera o ideal de identidades de uma subclasse das álgebras de Bernstein excepcionais
Title in English
not available
Abstract in English
This work is based on the paper Polynomial identities of Bernstein algebras of small dimension by J.Bernard, S.Gonzáles, C.Martinez and A.V. Iltyakov, published in the J.Algebra in 1998. We consider the Specht's problem, i.e., the problem of theexistence of a finite basis of (polynomial) identities for Bernstein algebras. In the first chapter we mention that this problem does not have solution for Bernstein algebras, has solution for Bernstein-Jordan algebras and for nuclear Bernsteinalgebras, and show that the ideal of identities of certain Bernstein algebra of dimension 2 has finite set of genarators. In the second chapter we find a finite set of identities which generates the ideal of identities of the class formed byregular Bernstein algebras. In the third chapter we find a finite set of identities which generates the ideal of identities of a subclass of exceptional Bernstein algebras
 
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Publishing Date
2021-07-29
 
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