This research extends hopf–galois extensions to infinite fields, revealing a galois correspondence.
This paper extends Hopf–Galois theory to infinite field extensions and provides a natural definition of subextensions. For separable (possibly infinite) Hopf–Galois extensions, it provides a Galois correspondence. This correspondence also is a refinement of what was known in the case of finite separable Hopf–Galois extensions.
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Bui et al. (2025) studied this question.
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