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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementA central simple algebra over an algebraic number field K which splits over every completion Kv is a matrix algebra over K. 1 Classification
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In Branch
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
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