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