Results 201 to 210 of about 40,312 (218)

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.
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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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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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Some Galois Extensions

1996
Now that we have developed the machinery of Galois theory, we apply it in this chapter to study special classes of field extensions. Sections 9 and 11 are good examples of how we can use group theoretic information to obtain results in field theory. Section 10 has a somewhat different flavor than the other sections.
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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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The commutator Hopf Galois extensions.

2019
Summary: Let \(H\) be a finite dimensional Hopf algebra over a field \(k\) and let \(H^*\) be the dual Hopf algebra of \(H\). Then a commutator right \(H^*\)-Galois extension \(B\) of \(B^H\) is characterized in terms of the smash product \(B\#H\). Some relationships between such extensions and the Hopf Galois Azumaya extensions or the Hopf Galois ...
Szeto, G., Xue, L.
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Galois Extensions

2017
Claudia Menini, Freddy Van Oystaeyen
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Galois extensions, Galois groups

2018
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