[Home]History of Field extension

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Revision 11 . . (edit) December 15, 2001 2:46 am by Zundark [degree of extension of extension]
Revision 10 . . December 14, 2001 10:55 pm by Zundark [Galois extensions, Abelian extensions]
Revision 9 . . (edit) December 14, 2001 9:34 pm by Zundark [a tiny bit more on simple extensions]
Revision 8 . . December 14, 2001 1:26 pm by AxelBoldt [K(V) improved]
Revision 7 . . December 14, 2001 5:24 am by AxelBoldt [L generated by V]
Revision 6 . . December 14, 2001 4:11 am by Zundark [simple extensions]
Revision 5 . . December 14, 2001 3:29 am by Zundark [pure transcendental + examples]
Revision 4 . . December 14, 2001 3:10 am by Zundark [algebraic & transcendental]
Revision 3 . . (edit) December 14, 2001 1:17 am by Zundark [change a link]
Revision 2 . . December 14, 2001 1:03 am by Zundark [add some simple examples]
Revision 1 . . December 14, 2001 12:06 am by Zundark [a start - more later (maybe)]
  
Difference (from prior major revision) (minor diff, author diff)

Changed: 7c7
The notation L/K is sometimes used to denote the fact that L is a extension of K.
The notation L/K is often used to denote the fact that L is a extension of K.

Added: 19a20,21
If M is an extension of L which is an extension of K,
then [M : K] = [M : L].[L : K].

Changed: 45c47,50
See also: Galois group
A field extension which has a Galois group is called a Galois extension.
If the Galois group is Abelian, then the extension is called an Abelian extension.
For example, C/R is a Abelian extension, its Galois group being of order 2.
But R/Q is not a Galois extension, as the only field automorphism of R is the identity automorphism.
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