Perfect field: Difference between revisions
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# Every [[irreducible polynomial]] over the field is a [[defining ingredient::separable polynomial]]. | # Every [[irreducible polynomial]] over the field is a [[defining ingredient::separable polynomial]]. | ||
===Equivalence of definitions=== | |||
{{further|[[Equivalence of definitions of perfect field]]}} | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 22:07, 14 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 perfect if it satisfies the following equivalent conditions:
- It is either a field of characteristic zero or it has characteristic for some prime , and the Frobenius map is surjective.
- Every finite extension of the field is a separable extension.
- Every irreducible polynomial over the field is a separable polynomial.
Equivalence of definitions
Further information: Equivalence of definitions of perfect field