Results 21 to 30 of about 316,648 (204)
On a notion of “Galois closure” for extensions of rings [PDF]
Journal of the European Mathematical Society, 2014 We introduce a notion of “Galois closure” for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an S_n degree n
Bhargava, Manjul, Satriano, Matthew
openaire +3 more sources
Normal Bases on Galois Ring Extensions [PDF]
Symmetry, 2018 In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(pr, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p} (q=p^n)$ by Theorem 1. We determine all optimal normal bases
Zhang Aixian, Feng Keqin
openaire +3 more sources
Galois lattice theory for probabilistic visual landmarks [PDF]
, 2004 This paper presents an original application of the Galois lattice theory, the visual landmark selection for topological localization of an autonomous mobile robot, equipped with a color camera.
Samuelides,Manuel +3 more
core +1 more source
Self-Dual Normal Basis of a Galois Ring
Journal of Mathematics, 2014 Let R′=GR(ps,psml) and R=GR(ps,psm) be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis for R′ over R, where R′ is ...
Irwansyah +3 more
doaj +1 more source
On Galois projective group rings
International Journal of Mathematics and Mathematical Sciences, 1991 Let A be a ring with 1, C the center of A and G′ an inner automorphism group of A induced by {Uα in A/α in a finite group G whose order is invertible}.
George Szeto, Linjun Ma
doaj +1 more source
Современная наука и инновации, 2022 When using a discrete Fourier transform (DFT) to solve digital signal processing (DSP) problems, errors occur in rounding or truncating the results of operations to the word length used by specialized processors (SP).
M. I. Kalmykov +3 more
doaj +1 more source
An overview over the Infinite Galois Theory and Absolute Galois Groups [PDF]
, 2023 openIn this thesis the generalization of classical Galois Theory to the case of infinite algebraic extensions is analyzed. The key point is the notion of Krull topology on groups, providing a Fundamental Theorem of Galois Theory for infinite extensions ...
ZANIN, GIOVANNI
core
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
openaire +1 more source
A Unique Representation of Cyclic Codes over GR(pn,r)
Axioms, 2022 Let R be a Galois ring, GR(pn,r), of characteristic pn and of order pnr. In this article, we study cyclic codes of arbitrary length, N, over R. We use discrete Fourier transform (DFT) to determine a unique representation of cyclic codes of length, N, in ...
Sami Alabiad, Yousef Alkhamees
doaj +1 more source
A Galois theory of commutative rings [PDF]
, 2005 Galois objects—Galois groups, rings, Lie rings, and birings G—act on commutative rings A and satisfy Galois correspondence theorems which support Galois descent. This generalizes the Galois theory of fields to a Galois theory of commutative rings.
Winter, David J.
core +1 more source