splitting field
Let be a polynomial over a field . A splitting field for is a field extension of such that
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1.
splits (factors into a product of linear factors) in ,
-
2.
is the smallest field with this property (any sub-extension field of which satisfies the first property is equal to ).
Theorem: Any polynomial over any field has a splitting field, and any two such splitting fields are isomorphic. A splitting field is always a normal extension of the ground field.
Title | splitting field |
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Canonical name | SplittingField |
Date of creation | 2013-03-22 12:08:01 |
Last modified on | 2013-03-22 12:08:01 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 7 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 12F05 |
Related topic | NormalExtension |