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Hopf-Galois structures on a Galois S-extension [PDF]

Journal of Algebra, 2019
In this paper, we shall determine the exact number of Hopf-Galois structures on a Galois $S_n$-extension, where $S_n$ denotes the symmetric group on $n$ letters.
Cindy Tsang
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Galois extensions and $$O^{*}$$-fields

Positivity, 2023
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Kenneth Evans, Jingjing Ma
openaire   +1 more source

Galois-type correspondences for Hopf Galois extensions

K-Theory, 1994
The authors construct a certain Hopf algebra associated with a commutative Galois extension in order to obtain a Galois correspondence between intermediate subalgebras of a Hopf-Galois extension and corresponding Hopf subalgebras.
Van Oystaeyen, Freddy, Zhang, Y.
openaire   +2 more sources

GALOIS CORRESPONDENCES FOR PARTIAL GALOIS AZUMAYA EXTENSIONS

Journal of Algebra and Its Applications, 2011
Let α be a partial action, having globalization, of a finite group G on a unital ring R. Let Rα denote the subring of the α-invariant elements of R and CR(Rα) the centralizer of Rα in R. In this paper we will show that there are one-to-one correspondences among sets of suitable separable subalgebras of R, Rα and CR(Rα). In particular, we extend to the
Paques, Antonio, Rodrigues, Virgínia, Sant'Ana, Alveri   +2 more
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Gradings of Galois Extensions

Journal of Mathematical Sciences
This paper deals with the gradings of finite field extensions in which all homogeneous components are one-dimensional. Such gradings are called \textit{fine}. Kummer extensions, obtained by adjoining roots of elements from the base field, admit a natural grading based on the Galois group, and all homogeneous components are one-dimensional in this case.
Badulin, D. A., Kanunnikov, A. L.
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On Galois extension of Hopf algebras

Chinese Annals of Mathematics, Series B, 2007
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Liu, Guohua, Zhu, Shenglin
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Azumaya Extensions and Galois Correspondence

Algebra Colloquium, 2000
For \(H\) a finite-dimensional Hopf algebra over a field \(k\), the author studies \(H^*\)-Galois Azumaya extensions \(A\) and obtains a Galois correspondence generalizing work of \textit{R. Alfaro} and \textit{G. Szeto} [in Rings, extensions and cohomology, Lect. Notes Pure Appl. Math. 159, 1-7 (1994; Zbl 0812.16038)] for group algebras.
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Galois Extensions of Boolean Algebras

Order, 1998
Recall that automorphisms \(f,g\) are strongly distinct if for every nonzero element there is an \(s\) such that \(f(s)\cdot b\not=g(s)\cdot b\). \(B\) is Galois over \(C\) if \(\text{Fix}(G)=C\) for some subgroup \(G\) of strongly distinct members of \(\text{Aut}_CB\). The author shows that a finite extension \(B\) is Galois over \(C\) if and only if \
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GALOIS EXTENSIONS OF RADICAL ALGEBRAS

Mathematics of the USSR-Sbornik, 1976
Suppose is a finite group of automorphisms of an associative algebra with an identity element over a field . Let . Assume that is a supernilpotent radical which is closed under the taking of subalgebras and satisfies the following condition: if and is a nonempty set, then the ring of matrices all but a finite number of whose columns are zero is radical.
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A Relational Extension of Galois Connections

2019
In this paper, we focus on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations as well.
Inma P. Cabrera, Pablo Cordero, Emilio Muñoz-Velasco, Manuel Ojeda-Aciego   +3 more
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