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Azumaya Extensions and Galois Correspondence
Algebra Colloquium, 2000For \(H\) 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, 1998Recall 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, 1976Suppose 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.
2019Summary: 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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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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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.
openaire +1 more source