Estudos sobre A-identidades polinomiais

The aim of this work is to study A-identities in associative algebras. More specifically, we study the A-identities of the tensor square of the unitary and infinite dimensional Grassmann algebra E, denoted by R, and we find the minimum degree of an A-identity of R. Due to Kemer's Tensor Product...

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Detalles Bibliográficos
Autor: Naves, Fernando Augusto
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2021
País:Brasil
Institución:Universidade Federal de São Carlos (UFSCAR)
Repositorio:Repositório Institucional da UFSCAR
Idioma:portugués
OAI Identifier:oai:repositorio.ufscar.br:20.500.14289/14762
Acceso en línea:https://repositorio.ufscar.br/handle/20.500.14289/14762
Access Level:acceso abierto
Palabra clave:PI-Álgebras
Álgebra graduada
Identidade polinomial
A-Identidade polinomial
Álgebra de Grassmann
Tensor Quadrado da Álgebra de Grassmann
PI-Algebras
Graded algebra
Polynomial identity
Polynomial A-identity
Grassmann algebra
Tensor Square of the Grassmann Algebra
CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA
Descripción
Sumario:The aim of this work is to study A-identities in associative algebras. More specifically, we study the A-identities of the tensor square of the unitary and infinite dimensional Grassmann algebra E, denoted by R, and we find the minimum degree of an A-identity of R. Due to Kemer's Tensor Product Theorem, in characteristic zero the algebras M_{1,1}(E) and R are PI-equivalent. Thus, in several moments we deal with the algebra M_{1,1}(E). In a second moment, we study the Z_2-graded A-identities of M_{1,1}(E). In this sense, we describe the set of such identities and calculate its respective graded A-codimensions.