Vipul: Created page with '{{field extension property}} ==Definition== ===Symbol-free definition=== A field extension is termed '''algebraic''' if it satisfies the following equivalent conditions: ...'

2009-05-10T16:46:50Z

Created page with '{{field extension property}} ==Definition== ===Symbol-free definition=== A field extension is termed '''algebraic''' if it satisfies the following equivalent conditions: ...'

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{{field extension property}}

==Definition==

===Symbol-free definition===

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

# Every element in the extension is algebraic over the base field.
# The sub-extension generated by any finite subset of the extension is a [[finite extension]] of the base field.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Galois extension]]
* [[Weaker than::Normal extension]]
* [[weaker than::Finite extension]]

Algebraic extension - Revision history

Vipul: Created page with '{{field extension property}} ==Definition== ===Symbol-free definition=== A field extension is termed '''algebraic''' if it satisfies the following equivalent conditions: ...'