A (finite) **separable algebra** $A$ over a field $F$, also called an **étale $F$-algebra**, is an $F$-algebra of finite dimension that is isomorphic to a product of separable field extensions of $F$.

If $L/K$ is a field extension and $A$ is a separable $K$-algebra then $A\otimes_K L$ is a separable $L$-algebra (which is typically not a field, even when $A$ is).

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- Review status: reviewed
- Last edited by David Roberts on 2019-05-03 20:36:52

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**History:**(expand/hide all)

- 2019-05-03 20:36:52 by David Roberts (Reviewed)
- 2019-05-03 18:52:28 by Andrew Sutherland
- 2019-05-03 18:49:07 by Andrew Sutherland
- 2019-05-03 18:43:45 by Andrew Sutherland
- 2017-09-06 19:47:00 by Andrew Sutherland

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