The Albert-Brauer-Hasse-Noether theorem is a result in algebraic number theory stating that a central simple algebra over an algebraic number field K that splits over every completion of K is in fact a matrix algebra over K itself. It is an example of a local-global principle, and it leads to a complete description of finite-dimensional division algebras over algebraic number fields in terms of their local invariants. The theorem was proved independently by Richard Brauer, Helmut Hasse and Emmy Noether, and separately by Abraham Adrian Albert.
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StatementA central simple algebra over an algebraic number field K which splits over every completion Kv is a matrix algebra over K. 1 Classification
Statement Form Albert-Brauer-Hasse-Noether Theorem
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Source Albert-Brauer-Hasse-Noether theorem (Wikipedia)
Principal Result Of
Source Albert-Brauer-Hasse-Noether Theorem (Wikipedia)
Source Albert-Brauer-Hasse-Noether Theorem (Wikipedia)
Proved By
Source Albert-Brauer-Hasse-Noether theorem (Wikipedia)
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1. Albert-Brauer-Hasse-Noether theorem (Wikipedia)
Introduction
a central simple algebra over an algebraic number field K which splits over every completion Kv is a matrix algebra over K
- In Branch: Algebraic Number Theory, Lead sentence
Proved By: Emmy Noether, Lead paragraph
proved independently by Richard Brauer, Helmut Hasse, and Emmy Noether
View the SourceAlbert-Brauer-Hasse-Noether Theorem (Wikipedia)
Principal Result Of: Richard Brauer, Lead sentence of the article on the result
It was proved independently by Richard Brauer, Helmut Hasse, and Emmy Noether and by Abraham Adrian Albert.
Principal Result Of: Helmut Hasse, Lead sentence of the article on the result
It was proved independently by Richard Brauer, Helmut Hasse, and Emmy Noether and by Abraham Adrian Albert.
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