 If the extension is finite and Galois, then formula_244 is canonically isomorphic to formula_248.Azumaya algebras generalize the notion of central simple algebras to a commutative local ring.If "K" is a field, a valuation "v" is a group homomorphism from the multiplicative group "K"* to a totally ordered abelian group "G" such that, for any "f", "g" in "K" with "f" + "g" nonzero, "v"("f" + "g") ≥ min{"v"("f"), "v"("g")}.