A generalization of Kummer theory to Hopf-Galois extensions

Separable extensions, Galois theory (12F10) Cyclotomic extensions (11R18) Ramification and extension theory (11S15) Algebraic numbers; rings of algebraic integers (11R04) Hopf algebras and their applications (16T05)

Cites Work

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Induced Hopf Galois structures
On the discriminant of a trinomial
Generalized Kummer theory and its applications
Arithmétique d'une extension galoisienne à groupe d'inertie cyclique
Normal integral bases in Kummer extensions of prime degree
On the ring of integers of a tame Kummer extension over a number field.
Commutative Hopf-Galois module structure of tame extensions
Hopf Galois theory for separable field extensions
How far is an extension of \(p\)-adic fields from having a normal integral basis?
Induced Hopf Galois structures and their local Hopf Galois modules
The ring of integers of Hopf-Galois degree \(p\) extensions of \(p\)-adic fields with dihedral normal closure
Hopf-Galois module structure of quartic Galois extensions of \(\mathbb{Q}\)
Hopf-Galois module structure of tamely ramified radical extensions of prime degree
Hopf-Galois structures on almost cyclic field extensions of 2-power degree
Generation of Galois extensions by matrix roots
Hopf algebras and Galois theory
On the linear independence of algebraic numbers
Normal integral bases for cyclic Kummer extensions
Normal integral bases and tameness conditions for Kummer extensions
From Galois to Hopf Galois: theory and practice
Cyclic Galois Extensions and Normal Bases
On subfÌields of radical extensions
Uniqueness of hopf galois structure for separable field extensions
The monogeneity of radical extensions
Hopf Algebras and Galois Module Theory
Normality and short exact sequences of Hopf-Galois structures

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