O número de classes do subcorpo real maximal de um corpo ciclotômico

• Autor(a) principal: Oliveira, Fernando Neres de
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/61329
• topic: Teoria dos números; Galois, Teoria de; Grupos abelianos

The aim of this paper is to present some results on the number of classes of real maximal subcorpo a body ciclotômico.Para this, we will first prove the finiteness of the group of classes of ideals and make a brief study of the decomposition of prime ideals in a extension. Following, we present the real subcorpo a maximal cyclotomic fields and will use some results on the characters and Gaussian sums, to justify the dumping of a body in a real quadratic subcorpo maximal real particular. After that, we present the results of two articles, the first of N. C. Ankeny, S. Chowla and H. Hasse, and the second of Hideo Yokoi. Both have the objective of studying the number of classes of real subcorpo a maximal cyclotomic fields.