Splitting field: Difference between revisions

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* {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | pages=235-237 }}
* {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | pages=235-237 }}
* {{ cite book | author=P.J. McCarthy | title=Algebraic extensions of fields | publisher=[[Dover Publications]] | year=1991 | isbn=0-486-66651-4 | pages=15-16 }}
* {{ cite book | author=P.J. McCarthy | title=Algebraic extensions of fields | publisher=[[Dover Publications]] | year=1991 | isbn=0-486-66651-4 | pages=15-16 }}
* {{cite book | author=I.N. Stewart | authorlink=Ian Stewart (mathematician) | title=Galois theory | publisher=Chapman and Hall | year=1973 | isbn=0-412-10800-3 | pages=86-90 }}
* {{cite book | author=I.N. Stewart | authorlink=Ian Stewart (mathematician) | title=Galois theory | publisher=Chapman and Hall | year=1973 | isbn=0-412-10800-3 | pages=86-90 }}[[Category:Suggestion Bot Tag]]

Latest revision as of 07:01, 21 October 2024

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In algebra, a splitting field for a polynomial f over a field F is a field extension E/F with the properties that f splits completely over E, but not any subfield of E containing F.

A splitting field for a given polynomial always exists, and is unique up to field isomorphism.

References