Vipul: Created page with '{{field extension property}} ==Definition== A field extension is termed a '''quadratic extension''' if it satisfies the following equivalent conditions: # It is the [[spli...'

2009-05-10T17:21:37Z

Created page with '{{field extension property}} ==Definition== A field extension is termed a '''quadratic extension''' if it satisfies the following equivalent conditions: # It is the [[spli...'

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{{field extension property}}

==Definition==

A [[field extension]] is termed a '''quadratic extension''' if it satisfies the following equivalent conditions:

# It is the [[splitting field]] for an irreducible polynomial of degree two.
# It is a extension of [[defining ingredient::degree of a field extension|degree]] two.
# It is a [[defining ingredient::normal extension]] of degree two.

==Relation with other properties==

===Weaker properties===

* [[Stronger than::Finite normal extension]]
* [[Stronger than::Finite extension]]
* [[Stronger than::Normal extension]]: {{proofat|[[Quadratic implies normal]]}}

Quadratic extension - Revision history

Vipul: Created page with '{{field extension property}} ==Definition== A field extension is termed a '''quadratic extension''' if it satisfies the following equivalent conditions: # It is the [[spli...'