Editing Split-quaternion (section)

{{Short description|Four-dimensional associative algebra over the reals}}
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In [[abstract algebra]], the '''split-quaternions'''  or '''coquaternions''' form an [[algebraic structure]] introduced by [[James Cockle (lawyer)|James Cockle]] in 1849 under the latter name. They form an [[associative algebra]] of dimension four over the [[real number]]s.

After introduction in the 20th century of coordinate-free definitions of [[ring (mathematics)|rings]] and [[algebra over a field|algebras]], it was proved that the algebra of split-quaternions is [[isomorphism|isomorphic]] to the [[ring (mathematics)|ring]] of the {{math|2×2}} [[real matrix|real matrices]]. So the study of split-quaternions can be reduced to the study of real matrices, and this may explain why there are few mentions of split-quaternions in the mathematical literature of the 20th and 21st centuries.