💡 — Historical Context Emmy Noether's formulation of these equations was part of a broader program to understand field extensions through the lens of group cohomology. What Artin presents here as Theorems 21 and 22 became foundational results in the cohomological approach to class field theory. The condition x_σ = a/σ(a) says that every 1-cocycle is a 1-coboundary -- in modern language, that H¹(G, E^×) = 0. 🔗 magicinternetmath.com 🏴‍☠️ Subscribe to the Pioneers Club ⚡ fundamentals@zeuspay.com #bitcoin #education