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Noether Equation on Artin and Milgram Galois Theory book
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On Section K Chapter 2 of Galois Book by Artin and Milgram it discusses Noether Equation, but I'm not sure what Noether Equation this is, I know about Noether Equation for symmetry in physics but not sure about one in relation to Galois Theory.
The book states that $x_sigma cdot sigma(x_tau ) = x_{sigma tau}$ satisfies Noether Equation where $sigma, tau$ are automorphisms of field $E$ and $x_sigma, x_tau in E$
If anyone knows what the Noether Equation they are referring to please elucidate :) Thanks in advance
galois-theory noetherian
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
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add a comment |
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On Section K Chapter 2 of Galois Book by Artin and Milgram it discusses Noether Equation, but I'm not sure what Noether Equation this is, I know about Noether Equation for symmetry in physics but not sure about one in relation to Galois Theory.
The book states that $x_sigma cdot sigma(x_tau ) = x_{sigma tau}$ satisfies Noether Equation where $sigma, tau$ are automorphisms of field $E$ and $x_sigma, x_tau in E$
If anyone knows what the Noether Equation they are referring to please elucidate :) Thanks in advance
galois-theory noetherian
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
$endgroup$
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That is the Noether equation they are talking about (it's a cocycle relation). Noether didn't just do one thing....
$endgroup$
– Lord Shark the Unknown
Jan 15 at 1:08
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Yes sorry this is a cocycle condition (Galois cohomology) that is a function $f : G to E^times$ such that $f(sigmatau )/f(sigma) = sigma (f(tau)/f(1))$ (which is a much weaker condition than $f(sigmatau )=sigma(f(tau ))$)
$endgroup$
– reuns
Jan 15 at 1:18
add a comment |
$begingroup$
On Section K Chapter 2 of Galois Book by Artin and Milgram it discusses Noether Equation, but I'm not sure what Noether Equation this is, I know about Noether Equation for symmetry in physics but not sure about one in relation to Galois Theory.
The book states that $x_sigma cdot sigma(x_tau ) = x_{sigma tau}$ satisfies Noether Equation where $sigma, tau$ are automorphisms of field $E$ and $x_sigma, x_tau in E$
If anyone knows what the Noether Equation they are referring to please elucidate :) Thanks in advance
galois-theory noetherian
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
$endgroup$
On Section K Chapter 2 of Galois Book by Artin and Milgram it discusses Noether Equation, but I'm not sure what Noether Equation this is, I know about Noether Equation for symmetry in physics but not sure about one in relation to Galois Theory.
The book states that $x_sigma cdot sigma(x_tau ) = x_{sigma tau}$ satisfies Noether Equation where $sigma, tau$ are automorphisms of field $E$ and $x_sigma, x_tau in E$
If anyone knows what the Noether Equation they are referring to please elucidate :) Thanks in advance
galois-theory noetherian
galois-theory noetherian
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
asked Jan 14 at 22:45
john takeuchijohn takeuchi
313
313
$begingroup$
That is the Noether equation they are talking about (it's a cocycle relation). Noether didn't just do one thing....
$endgroup$
– Lord Shark the Unknown
Jan 15 at 1:08
$begingroup$
Yes sorry this is a cocycle condition (Galois cohomology) that is a function $f : G to E^times$ such that $f(sigmatau )/f(sigma) = sigma (f(tau)/f(1))$ (which is a much weaker condition than $f(sigmatau )=sigma(f(tau ))$)
$endgroup$
– reuns
Jan 15 at 1:18
add a comment |
$begingroup$
That is the Noether equation they are talking about (it's a cocycle relation). Noether didn't just do one thing....
$endgroup$
– Lord Shark the Unknown
Jan 15 at 1:08
$begingroup$
Yes sorry this is a cocycle condition (Galois cohomology) that is a function $f : G to E^times$ such that $f(sigmatau )/f(sigma) = sigma (f(tau)/f(1))$ (which is a much weaker condition than $f(sigmatau )=sigma(f(tau ))$)
$endgroup$
– reuns
Jan 15 at 1:18
$begingroup$
That is the Noether equation they are talking about (it's a cocycle relation). Noether didn't just do one thing....
$endgroup$
– Lord Shark the Unknown
Jan 15 at 1:08
$begingroup$
That is the Noether equation they are talking about (it's a cocycle relation). Noether didn't just do one thing....
$endgroup$
– Lord Shark the Unknown
Jan 15 at 1:08
$begingroup$
Yes sorry this is a cocycle condition (Galois cohomology) that is a function $f : G to E^times$ such that $f(sigmatau )/f(sigma) = sigma (f(tau)/f(1))$ (which is a much weaker condition than $f(sigmatau )=sigma(f(tau ))$)
$endgroup$
– reuns
Jan 15 at 1:18
$begingroup$
Yes sorry this is a cocycle condition (Galois cohomology) that is a function $f : G to E^times$ such that $f(sigmatau )/f(sigma) = sigma (f(tau)/f(1))$ (which is a much weaker condition than $f(sigmatau )=sigma(f(tau ))$)
$endgroup$
– reuns
Jan 15 at 1:18
add a comment |
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$begingroup$
That is the Noether equation they are talking about (it's a cocycle relation). Noether didn't just do one thing....
$endgroup$
– Lord Shark the Unknown
Jan 15 at 1:08
$begingroup$
Yes sorry this is a cocycle condition (Galois cohomology) that is a function $f : G to E^times$ such that $f(sigmatau )/f(sigma) = sigma (f(tau)/f(1))$ (which is a much weaker condition than $f(sigmatau )=sigma(f(tau ))$)
$endgroup$
– reuns
Jan 15 at 1:18