Results 21 to 30 of about 40,145 (217)
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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Skew group rings which are Galois
International Journal of Mathematics and Mathematical Sciences, 2000 Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG.
George Szeto, Lianyong Xue
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Some interactions between Hopf Galois extensions and noncommutative rings
Universitas Scientiarum, 2022 In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW ...
Armando Reyes, Fabio Calderón
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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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On generalized Hopf galois extensions
Journal of Pure and Applied Algebra, 2005 23 ...
Schauenburg, Peter +1 more
openaire +3 more sources
Separable subalgebras of a class of Azumaya algebras
International Journal of Mathematics and Mathematical Sciences, 1998 Let S be a ring with 1, C the center of S, G a finite automorphism group of S of order n invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the skew group ring S*G is a G′-Galois extension of (S*G)G′ that
George Szeto
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The Boolean algebra of Galois algebras
International Journal of Mathematics and Mathematical Sciences, 2003 Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}.
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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, 2017 In this paper, we develop a difference Galois theory in the setting of real fields. After proving the existence and uniqueness of the real Picard-Vessiot extension, we define the real difference Galois group and prove a Galois correspondence.Comment ...
Dreyfus, Thomas
core +2 more sources