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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| 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 |
| 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. |
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