Splitting field

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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

• A.G. Howson (1972). A handbook of terms used in algebra and analysis. Cambridge University Press, 72. ISBN 0-521-09695-2. 
• Serge Lang (1993). Algebra, 3rd ed. Addison-Wesley, 235-237. ISBN 0-201-55540-9. 
• P.J. McCarthy (1991). Algebraic extensions of fields. Dover Publications, 15-16. ISBN 0-486-66651-4. 
• I.N. Stewart (1973). Galois theory. Chapman and Hall, 86-90. ISBN 0-412-10800-3.