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→Quaternion algebras over the rational numbers: fixing redlink by linking to the singular rather than plural form: unit groups → unit groups |
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{{Short description|generalization of quaternions to other fields}}
In [[mathematics]], a '''quaternion algebra''' over a field ''F'' is a [[central simple algebra]] ''A'' over ''F''<ref>See Peirce. Associative algebras. Springer. Lemma at page 14.</ref><ref>See Milies & Sehgal, An introduction to group rings, exercise 17, chapter 2.</ref> that has dimension 4 over ''F''. Every quaternion algebra becomes the matrix algebra by ''[[Scalar extension|extending scalars]]'' (equivalently, [[tensor product of algebras|tensoring]] with a field extension), i.e. for a suitable [[field extension]] ''K'' of ''F'', <math>A \otimes_F K</math> is isomorphic to the 2×2 [[matrix algebra]] over ''K''.
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