ABSTRACT
The fundamental property of Cogalois extensions says that any such extension E/F is an extension with https://www.w3.org/1998/Math/MathML"> T ( E / F ) / F * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq4159.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -Cogalois correspondence (Theorem 3.2.3 (1)); in other words, an extension with https://www.w3.org/1998/Math/MathML"> T ( E / F ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175695/6f0d74fd-b81c-4cd4-b8d9-805c7c0522ee/content/eq4160.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -Cogalois extension. We show in this chapter that this is an immediate consequence of the n-Purity Criterion we proved in Section 4.3.
