Results 11 to 20 of about 39,323 (189)
The Galois algebras and the Azumay Galois extensions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K={g∈G|g(c)=c for all c∈C}, Jg{b∈B|bx=g(x)b for all x∈B} for each g∈K, and BK=(⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by
George Szeto, Lianyong Xue
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On Hopf Galois Hirata extensions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 Let H be a finite-dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*-Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB ...
George Szeto, Lianyong Xue
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On the Characterization of Galois Extensions [PDF]
The American Mathematical Monthly, 2014 We present a shortcut to the familiar characterizations of finite Galois extensions, based on an idea from an earlier Monthly note by Sonn and Zassenhaus.
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Generic Galois extensions [PDF]
Proceedings of the National Academy of Sciences, 1980 We define the notion of a generic Galois extension with group G over a field F . Let R be a communtative ring of the form F [ x 1 ,..., x n ](1/
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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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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 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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An Efficient Audio Encryption Scheme Based on Finite Fields
IEEE Access, 2021 Finite fields are well-studied algebraic structures with enormous efficient properties which have applications in the fields of cryptology and coding theory.
Dawood Shah +5 more
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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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Polynomial composites and certain types of fields extensions
Karpatsʹkì Matematičnì Publìkacìï, 2023 In this paper, we consider polynomial composites with the coefficients from $K\subset L$. We already know many properties, but we do not know the answer to the question of whether there is a relationship between composites and field extensions.
Ł. Matysiak
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