Results 21 to 30 of about 694,433 (211)
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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On Galois matrix rings of a ring
Gulf Journal of Mathematics, 2013 Let R be a ring with 1, Mn(R) the ring of n × n-matrices over R for an integer n, and G an inner automorphism group of Mn(R) of order n2 induced by {Ui ∈ Mn(R), i = 1, ... , n2}. Then the Galois matrix ring Mn(R) over R with inner Galois group G is characterized in terms of {Ui} and the trace of G.
George Szeto, Xiaolong Jiang
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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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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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Global Solvably Closed Anabelian Geometry [PDF]
, 2006 In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have ...
Mochizuki, Shinichi
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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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Polynomials with minimal value set over Galois rings
International Journal of Mathematics and Mathematical Sciences, 1991 Let GR(pn,m) denote the Galois ring of order pn,m, where p is a prime. In this paper we define and characterize minimal value set polynomials over GR(pn,m).
Maria T. Acosta-De-Orozco +1 more
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Journal of Mathematics, 2022 Let R0=GRpkr,pk be a Galois maximal subring of R so that R=R0⊕U⊕V⊕W⊕Y, where U,V,W, and Y are R0/pR0 spaces considered as R0-modules, generated by the sets u1,⋯,ue,v1,⋯,vf,w1,⋯,wg, and y1,⋯,yh, respectively.
Hezron Saka Were, Maurice Owino Oduor
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