Submitted by Eduardo Bruno Pedrozo (edulimaseixas@hotmail.com) on 2018-10-03T02:49:50Z No. of bitstreams: 3 Ata de Defesa - Eduardo Bruno.pdf: 444725 bytes, checksum: e4484ad3e7fb48901a81ce9c9a9d4584 (MD5) Carta Internet.pdf: 35030 bytes, checksum: 84d2885e4567e02da9a872369d54a8ad (MD5) Dissertação Eduardo Bruno.pdf: 755531 bytes, checksum: 021e6a1c8d4c5b4046b6a6445ee11ae1 (MD5) / Approved for entry into archive by PPGM Matemática (ppgmufam@gmail.com) on 2018-10-03T12:07:58Z (GMT) No. of bitstreams: 3 Ata de Defesa - Eduardo Bruno.pdf: 444725 bytes, checksum: e4484ad3e7fb48901a81ce9c9a9d4584 (MD5) Carta Internet.pdf: 35030 bytes, checksum: 84d2885e4567e02da9a872369d54a8ad (MD5) Dissertação Eduardo Bruno.pdf: 755531 bytes, checksum: 021e6a1c8d4c5b4046b6a6445ee11ae1 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-10-03T14:07:21Z (GMT) No. of bitstreams: 3 Ata de Defesa - Eduardo Bruno.pdf: 444725 bytes, checksum: e4484ad3e7fb48901a81ce9c9a9d4584 (MD5) Carta Internet.pdf: 35030 bytes, checksum: 84d2885e4567e02da9a872369d54a8ad (MD5) Dissertação Eduardo Bruno.pdf: 755531 bytes, checksum: 021e6a1c8d4c5b4046b6a6445ee11ae1 (MD5) / Made available in DSpace on 2018-10-03T14:07:21Z (GMT). No. of bitstreams: 3 Ata de Defesa - Eduardo Bruno.pdf: 444725 bytes, checksum: e4484ad3e7fb48901a81ce9c9a9d4584 (MD5) Carta Internet.pdf: 35030 bytes, checksum: 84d2885e4567e02da9a872369d54a8ad (MD5) Dissertação Eduardo Bruno.pdf: 755531 bytes, checksum: 021e6a1c8d4c5b4046b6a6445ee11ae1 (MD5) Previous issue date: 2017-09-01 / In this work we will prove a theorem of Richard Brauer on the index and the period of central simple algebras. A central simple algebra is a finite-dimensional algebra over a field that becomes isomorphic to a matrix algebra after extending scalars to a finite field extension. Wedderburn’s theorem allows us define an invariant of such an algebra, called the index and the Brauer group provides a classification of central simple algebras over a given field. The period of a central simple algebra is the order of its class in the Brauer group. Brauer’s theorem of 1929 shows that the period of a central simple algebra always divides its index, which is the main result of this work. Our proof is based on techniques from Galois cohomology. / Neste trabalho provamos um teorema de Richard Brauer sobre o´ındice e o per´ıodo de a´lgebras simples centrais. Uma a´lgebra simples central ´e uma a´lgebra de dimensa˜o finita sobre um corpo que se torna isomorfa a uma ´algebra de matrizes apo´s extensa˜o de escalares a uma extens˜ao finita de corpos. O teorema de Wedderburn nos permite definir um invariante de uma tal a´lgebra, dito o ´ındice e o grupo de Brauer fornece uma classifica¸ca˜o destas ´algebras sobre um corpo dado. O per´ıodo de uma a´lgebra simples central ´e a ordem da sua classe no grupo de Brauer. O teorema de Brauer de 1929 mostra que o per´ıodo de uma ´algebra simples central sempre divide o seu ´ındice, que ´e o resultado principal deste trabalho. Este teorema permite compreender melhor a estrutura destas a´lgebras. A nossa prova ´e baseada em t´ecnicas da cohomologia galoisiana.