Specialization of Quadratic and Symmetric Bilinear Forms [recurso electrónico] / by Manfred Knebusch.

Por: Knebusch, Manfred [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoSeries Algebra and Applications ; 11Editor: London : Springer London : Imprint: Springer, 2010Descripción: XIV, 192 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9781848822429Tema(s): Mathematics | Algebra | Mathematics | AlgebraFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512 Clasificación LoC:QA150-272Recursos en línea: Libro electrónicoTexto
Contenidos:
Fundamentals of Specialization Theory -- Generic Splitting Theory -- Some Applications -- Specialization with Respect to Quadratic Places.
En: Springer eBooksResumen: The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed mainly for fields of characteristic different from 2, are explored here without this restriction. In this book, a quadratic form f over a field of characteristic 2 is allowed to have a big quasilinear part QL(f) (defined as the restriction of f to the radical of the bilinear form associated to f), while in most of the literature QL(f) is assumed to have dimension at most 1. Of course, in nature, quadratic forms with a big quasilinear part abound. In addition to chapters on specialization theory, generic splitting theory and their applications, the book's final chapter contains research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.
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Colección de Libros Electrónicos QA150 -272 (Browse shelf(Abre debajo)) 1 No para préstamo 372707-2001

Fundamentals of Specialization Theory -- Generic Splitting Theory -- Some Applications -- Specialization with Respect to Quadratic Places.

The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed mainly for fields of characteristic different from 2, are explored here without this restriction. In this book, a quadratic form f over a field of characteristic 2 is allowed to have a big quasilinear part QL(f) (defined as the restriction of f to the radical of the bilinear form associated to f), while in most of the literature QL(f) is assumed to have dimension at most 1. Of course, in nature, quadratic forms with a big quasilinear part abound. In addition to chapters on specialization theory, generic splitting theory and their applications, the book's final chapter contains research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.

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