Separably closed field: Difference between revisions
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Revision as of 17:24, 10 May 2009
This article defines a field property: a property that can be evaluated to true/false for any field.
View a complete list of field properties|View a complete list of field extension properties
Definition
A field is termed separably closed if it satisfies the following equivalent conditions:
- Every irreducible polynomial over it that is separable is linear.
- It has no proper algebraic extension that is separable.
For any field, we can define the separable closure of the field, which is the unique smallest separably closed field containing it.