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On Galois and locally Galois extensions of simple rings
On Galois and locally Galois extensions of simple ringsopenaire
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Multiplication in a Galois ring
2015 Seventh International Workshop on Signal Design and its Applications in Communications (IWSDA), 2015In this paper, we focus on the efficient multiplication in a Galois ring of the size 4n, where n is a positive integer. We consider to adapt the finite field multiplication methods to the Galois ring multiplication. We give the polynomial multiplication in the Galois ring as a Toeplitz matrix-vector multiplication design with a modification used in ...
Sedat Akleylek, Ferruh Özbudak
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The Annals of Mathematics, 1996
This paper is concerned with the connections between the Witt ring of a field and the structure of certain Galois extensions of that field. In particular, it is shown that the Witt ring determines, and is determined by, the Galois group of a certain 2-extension of the field (with an unavoidable uncertainty over the characteristic of the Witt ring in ...
Mináč, Ján, Spira, Michel
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This paper is concerned with the connections between the Witt ring of a field and the structure of certain Galois extensions of that field. In particular, it is shown that the Witt ring determines, and is determined by, the Galois group of a certain 2-extension of the field (with an unavoidable uncertainty over the characteristic of the Witt ring in ...
Mináč, Ján, Spira, Michel
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Conversion of Element Representations in Galois Rings
Mathematics in Computer Science, 2020Let \(G(p^s,m)\) be a Galois ring. Each element in \(G(p^s,m)\) has an additive representation and a \(p\)-adic representation. In this paper, the authors develops a series of programs allowing the convertion between these two representations in a Galois ring.
Juan Carlos Ku-Cauich +1 more
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Discrete Mathematics and Applications, 2002
Abstract The aim of this paper is to introduce the notion of a generalised Galois ring, that is, a Galois ring without associativity assumptions. Some basic properties of associative Galois rings such as cardinality, characteristic, and ideal lattice structure are extended to the nonassociative case.
González, S. +4 more
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Abstract The aim of this paper is to introduce the notion of a generalised Galois ring, that is, a Galois ring without associativity assumptions. Some basic properties of associative Galois rings such as cardinality, characteristic, and ideal lattice structure are extended to the nonassociative case.
González, S. +4 more
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Decomposition of Witt Rings and Galois Groups
Canadian Journal of Mathematics, 1995AbstractTo each fieldFof characteristic not 2, one can associate a certain Galois group 𝒢F, the so-calledW-group ofF, which carries essentially the same information as the Witt ringW(F)ofF. In this paper we show that direct products of Witt rings correspond to free products of these Galois groups (in the appropriate category), group ring construction ...
Mináč, Ján, Smith, Tara L.
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