Results 1 to 10 of about 408 (185)
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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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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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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Designing a Block Cipher in Galois Extension Fields for IoT Security
IoT, 2021 This paper focuses on a block cipher adaptation of the Galois Extension Fields (GEF) combination technique for PRNGs and targets application in the Internet of Things (IoT) space, an area where the combination technique was concluded as a quality stream ...
Kiernan George, Alan J. Michaels
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Hopf Differential Graded Galois Extensions
Mathematics, 2022 We introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra H and an H-module dg algebra R, we show that D(R#H)≅D(RH) is equivalent to that R/RH is a Hopf differential graded Galois extension.
Bo-Ye Zhang
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Gorenstein Flat Modules of Hopf-Galois Extensions
Mathematics, 2023 Let A/B be a right H-Galois extension over a semisimple Hopf algebra H. The purpose of this paper is to give the relationship of Gorenstein flat dimensions between the algebra A and its subalgebra B, and obtain that the global Gorenstein flat dimension ...
Qiaoling Guo +3 more
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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
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On Azumaya Galois extensions and skew group rings
International Journal of Mathematics and Mathematical Sciences, 1999 Two characterizations of an Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special Galois system is determined by the trace of the Galois
George Szeto
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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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