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It was defined by the algebraist Richard Brauer. The Brauer group arose out of attempts to classify division algebras over a field. It can also be defined in terms of Galois cohomology. 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href="http://dbpedia.org/resource/Brauer_group">Brauer group</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/ontology/Band">Band</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer. The Brauer group arose out of attempts to classify division algebras over a field. It can also be defined in terms of Galois cohomology. More generally, the Brauer group of a scheme is defined in terms of Azumaya algebras, or equivalently using projective bundles. </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Die Brauergruppe wurde in der Mathematik eingeführt, um assoziative Divisionsalgebren über einem gegebenen Körper zu klassifizieren, die das Zentrum haben. Es handelt sich dabei um eine abelsche Gruppe, deren Elemente Äquivalenzklassen bestimmter Algebren sind. In der Literatur wird sie deshalb auch brauersche Algebrenklassengruppe genannt. Benannt ist sie nach dem Algebraiker Richard Brauer. (de)</li> <li>In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer. The Brauer group arose out of attempts to classify division algebras over a field. It can also be defined in terms of Galois cohomology. More generally, the Brauer group of a scheme is defined in terms of Azumaya algebras, or equivalently using projective bundles. (en)</li> <li style="display:none;">En mathématiques, le groupe de Brauer, nommé d'après Richard Brauer, constitue l'espace classifiant des algèbres centrales simples sur un corps commutatif k donné, pour une certaine relation d'équivalence. On munit cet espace d'une structure de groupe abélien en l'identifiant à un espace de cohomologie galoisienne. (fr)</li> <li style="display:none;">数学において、体 K に対するブラウアーの多元環類群（たげんかんるい、英: algebra class group）あるいは単に K のブラウアー群（ブラウアーぐん、英: Brauer group）Br(K) は、体 K 上の中心的単純環の森田同値類（多元環類、ブラウアー類）を元とするアーベル群で、その演算は多元環のテンソル積から誘導される。ブラウアー群は体上の斜体の分類の過程で考え出されたもので、名称は代数学者のに由来する。さらに一般に、スキームのブラウアー群の概念も（東屋代数）を用いて定義される。 (ja)</li> <li style="display:none;">In de abstracte algebra, een deelgebied van de wiskunde, is de Brauer-groep ontstaan uit een poging om de delingsalgebra's over een lichaam (Ned) / veld (Be) te classificeren. Een Brauer-groep is een abelse groep met elementen die equivalentieklassen van Azumaya-algebra's zijn, eindig-dimensionale enkelvoudige delingsalgebra's over , zodanig dat het centrum precies is. De Brauer-groep is naar de Duitse wiskundige Richard Brauer genoemd. (nl)</li> <li style="display:none;">У математиці групою Брауера поля k називається група класів еквівалентності скінченновимірних центральних простих алгебр над полем k із груповою операцією заданою тензорним добутком. Група Брауера була визначена і вивчалася в серії робіт Брауера, Нетер, Алберта, Хассе і інших починаючи з 20-х років 20 століття. Найповніші результати, аж до повного обчислення групи Брауера, були отримані для числових полів у зв'язку з розвитком теорії полів класів. У термінах групи Брауера формулюється загальна форма закону взаємності. Узагальненням поняття групи Брауера є група Брауера — Гротендіка, що визначається аналогічно група Брауера з заміною центральних простих алгебр на алгебри Адзумаї. (uk)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink">dbo:wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://archive.org/details/etalecohomology00miln" href="https://archive.org/details/etalecohomology00miln">https://archive.org/details/etalecohomology00miln</a></li> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://www.math.columbia.edu/~dejong/papers/2-gabber.pdf" href="http://www.math.columbia.edu/~dejong/papers/2-gabber.pdf">http://www.math.columbia.edu/~dejong/papers/2-gabber.pdf</a></li> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://www.math.jussieu.fr/~leila/grothendieckcircle/DixExp.pdf" href="http://www.math.jussieu.fr/~leila/grothendieckcircle/DixExp.pdf">http://www.math.jussieu.fr/~leila/grothendieckcircle/DixExp.pdf</a></li> <li><a class="uri" 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Iskovskikh (en)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/id">dbp:id</a> </td><td class="col-10 text-break"><ul> <li>B/b017610 (en)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/title">dbp:title</a> </td><td class="col-10 text-break"><ul> <li>Brauer group of a field k (en)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/wikiPageUsesTemplate">dbp:wikiPageUsesTemplate</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Citation" href="http://dbpedia.org/resource/Template:Citation">dbt:Citation</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Cite_book" href="http://dbpedia.org/resource/Template:Cite_book">dbt:Cite_book</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Reflist" href="http://dbpedia.org/resource/Template:Reflist">dbt:Reflist</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Short_description" href="http://dbpedia.org/resource/Template:Short_description">dbt:Short_description</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Eom" href="http://dbpedia.org/resource/Template:Eom">dbt:Eom</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://purl.org/dc/terms/subject">dcterms:subject</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Ring_theory" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Ring_theory">dbc:Ring_theory</a></li> <li><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Topological_methods_of_algebraic_geometry" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Topological_methods_of_algebraic_geometry">dbc:Topological_methods_of_algebraic_geometry</a></li> <li><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Algebraic_number_theory" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Algebraic_number_theory">dbc:Algebraic_number_theory</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://purl.org/linguistics/gold/hypernym">gold:hypernym</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="gold:hypernym" resource="http://dbpedia.org/resource/Group" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Group">dbr:Group</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/1999/02/22-rdf-syntax-ns#type">rdf:type</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/ontology/Band" href="http://dbpedia.org/ontology/Band">dbo:Band</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Die Brauergruppe wurde in der Mathematik eingeführt, um assoziative Divisionsalgebren über einem gegebenen Körper zu klassifizieren, die das Zentrum haben. Es handelt sich dabei um eine abelsche Gruppe, deren Elemente Äquivalenzklassen bestimmter Algebren sind. In der Literatur wird sie deshalb auch brauersche Algebrenklassengruppe genannt. Benannt ist sie nach dem Algebraiker Richard Brauer. (de)</li> <li>In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer. The Brauer group arose out of attempts to classify division algebras over a field. It can also be defined in terms of Galois cohomology. More generally, the Brauer group of a scheme is defined in terms of Azumaya algebras, or equivalently using projective bundles. (en)</li> <li style="display:none;">En mathématiques, le groupe de Brauer, nommé d'après Richard Brauer, constitue l'espace classifiant des algèbres centrales simples sur un corps commutatif k donné, pour une certaine relation d'équivalence. On munit cet espace d'une structure de groupe abélien en l'identifiant à un espace de cohomologie galoisienne. (fr)</li> <li style="display:none;">数学において、体 K に対するブラウアーの多元環類群（たげんかんるい、英: algebra class group）あるいは単に K のブラウアー群（ブラウアーぐん、英: Brauer group）Br(K) は、体 K 上の中心的単純環の森田同値類（多元環類、ブラウアー類）を元とするアーベル群で、その演算は多元環のテンソル積から誘導される。ブラウアー群は体上の斜体の分類の過程で考え出されたもので、名称は代数学者のに由来する。さらに一般に、スキームのブラウアー群の概念も（東屋代数）を用いて定義される。 (ja)</li> <li style="display:none;">In de abstracte algebra, een deelgebied van de wiskunde, is de Brauer-groep ontstaan uit een poging om de delingsalgebra's over een lichaam (Ned) / veld (Be) te classificeren. Een Brauer-groep is een abelse groep met elementen die equivalentieklassen van Azumaya-algebra's zijn, eindig-dimensionale enkelvoudige delingsalgebra's over , zodanig dat het centrum precies is. De Brauer-groep is naar de Duitse wiskundige Richard Brauer genoemd. (nl)</li> <li style="display:none;">У математиці групою Брауера поля k називається група класів еквівалентності скінченновимірних центральних простих алгебр над полем k із груповою операцією заданою тензорним добутком. Група Брауера була визначена і вивчалася в серії робіт Брауера, Нетер, Алберта, Хассе і інших починаючи з 20-х років 20 століття. Найповніші результати, аж до повного обчислення групи Брауера, були отримані для числових полів у зв'язку з розвитком теорії полів класів. У термінах групи Брауера формулюється загальна форма закону взаємності. 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