Talk:Galois module

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What is the G for which we are considering O_L as an O_K[G]-module?

The Galois group of L over K. Charles Matthews 09:40, 27 May 2004 (UTC)

[edit] Noether's theorem

"Then Noether's theorem states that tame ramification is necessary and sufficient for O_L to be a projective module over Z[G]. It is certainly therefore necessary for it to be a free module." Not every projective module is free, so these two sentences are confusing when taken together. Not familiar with Noether's theorem so can't correct it. Someone please fix. 74.112.174.192 14:37, 3 April 2007 (UTC)

Tame ramification is necessary to be projective. Free is a stronger condition than projective. So tame ramification is necessary to be free. Charles Matthews 19:39, 3 April 2007 (UTC)