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ehrenfest
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[SOLVED] extension fields
Let F be a field and let E be an extension field of F. Let [itex]\alpha[/itex] be an element of E that is algebraic over E. Is it true that all of the zeros of [itex]irr(\alpha,F)[/itex] are contained in the extension field [itex]F(\alpha)[/itex]?
EDIT: I mean algebraic over F
Homework Statement
Let F be a field and let E be an extension field of F. Let [itex]\alpha[/itex] be an element of E that is algebraic over E. Is it true that all of the zeros of [itex]irr(\alpha,F)[/itex] are contained in the extension field [itex]F(\alpha)[/itex]?
EDIT: I mean algebraic over F
Homework Equations
The Attempt at a Solution
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