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Quaternion algebra

In mathematics, a quaternion algebra over a fieldF is a central simple algebraA over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, A⊗FK{\displaystyle A\otimes _{F}K} is isomorphic to the 2 × 2 matrix algebra over K. The notion of a quaternion algebra can be seen as a generalization of Hamilton's quaternions to an arbitrary base field.

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