Results 31 to 40 of about 30,150 (231)
Galois groups over rational function fields over skew fields
Comptes Rendus. Mathématique, 2020 Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field.
Alon, Gil +2 more
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Generalized affine transformation monoids on Galois rings
International Journal of Mathematics and Mathematical Sciences, 2006 Let A be a ring with identity. The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form x↦xu+a (for all x∈A), where u,a∈A.
Yonglin Cao
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An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities
Mathematical and Computational Applications, 2018 Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities.
Juan Carlos Ku-Cauich +2 more
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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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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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True Random Number Generator Based on Fibonacci-Galois Ring Oscillators for FPGA
Applied Sciences, 2021 Random numbers are widely employed in cryptography and security applications. If the generation process is weak, the whole chain of security can be compromised: these weaknesses could be exploited by an attacker to retrieve the information, breaking even
Pietro Nannipieri +6 more
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A Galois Theory for Noncommutative Rings [PDF]
Transactions of the American Mathematical Society, 1967 hntroduction. In 1944, Jacobson [4] developed a Galois theory for nonnormal and nonseparable fields; and, in 1949, Hochschild [3] used the techniques of Jacobson to present a Galois theory for division rings. These same techniques will be used in this paper to present a Galois theory for rings with identity element.
openaire +1 more source
On weak center Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2001 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, the notion of a center Galois extension of BG with Galois group G (i.e., C is a Galois algebra over CG ...
George Szeto, Lianyong Xue
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Forum of Mathematics, Sigma, 2023 Let K be a finite extension of the p-adic field ${\mathbb {Q}}_p$ of degree d, let ${{\mathbb {F}}\,\!{}}$ be a finite field of characteristic p and let ${\overline {{D}}}$ be an n-dimensional pseudocharacter in the sense of ...
Gebhard Böckle, Ann-Kristin Juschka
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, 2010 Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also polynomial.
Fleischmann, Peter, Woodcock, Chris
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