Results 11 to 20 of about 271 (183)
On certain classes of Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2001 Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions.
George Szeto, Lianyong Xue
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Infinite Towers of Galois Defect Extensions of Kaplansky Fields
Annales Mathematicae Silesianae, 2018 We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of ...
Blaszczok Anna
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Hopf Quasigroup Galois Extensions and a Morita Equivalence
Mathematics, 2023 For H, a Hopf coquasigroup, and A, a left quasi-H-module algebra, we show that the smash product A#H is linked to the algebra of H invariants AH by a Morita context.
Huaiwen Guo, Shuanhong Wang
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On Galois Extension of Rings [PDF]
Nagoya Mathematical Journal, 1966 Let Λ be a ring and G a finite group of ring automorphisms of Λ. The totality of elements of Λ which are left invariant by G is a subring of Λ. We call it the G-fixed subring of Λ. Let be the crossed product of Λ and G with trivial factor set, i.e. {u0} is a Λ-free basis of Δ and , and let Γ be a subring of the G-fixed subring of Λ which has the same ...
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On central commutator Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2000 Let B be a ring with 1, G a finite automorphism group of B of order n for some integer n, BG the set of elements in B fixed under each element in G, and Δ=VB(BG) the commutator subring of BG in B.
George Szeto, Lianyong Xue
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On characterizations of a center Galois extension
International Journal of Mathematics and Mathematical Sciences, 2000 Let B be a ring with 1, C the center of B, G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. Then, it is shown that B is a center Galois extension of BG (that is, C is a Galois algebra over CG with ...
George Szeto, Lianyong Xue
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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.
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On generalized Hopf galois extensions
Journal of Pure and Applied Algebra, 2005 23 ...
Schauenburg, Peter +1 more
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Galois extensions and a conjecture of Ogg
Proceedings of the American Mathematical Society, 2020 Let N = p q N=pq
Klosin, Krzysztof, Papikian, Mihran
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On automorphism group of free quadratic extensions over a ring
International Journal of Mathematics and Mathematical Sciences, 1984 Let R be a ring with 1, ρ an automorphism of R of order 2. Then a normal extension of the free quadratic extension R[x,ρ] with a basis {1,x} over R with an R-automorphism group G is characterized in terms of the element (x−(x)α) for α in G.
George Szeto
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