Results 31 to 40 of about 1,203,239 (192)

Twisting commutative algebraic groups [PDF]

, 2007
If $V$ is a commutative algebraic group over a field $k$, $O$ is a commutative ring that acts on $V$, and $I$ is a finitely generated free $O$-module with a right action of the absolute Galois group of $k$, then there is a commutative algebraic group $I \
Mazur, B., Rubin, K., Silverberg, A.
core   +2 more sources

Short Principal Ideal Problem in multicubic fields

Journal of Mathematical Cryptology, 2020
One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices.
Lesavourey Andrea, Plantard Thomas, Susilo Willy   +2 more
doaj   +1 more source

Fermat–Euler Theorem in Algebraic Number Fields [PDF]

, 1996
In this paper a (maximal) generalization of the classical Fermat–Euler theorem for finite commutative rings with identity is proved. Maximal means that we show how to extend the original Fermat–Euler theorem to all of the elements of such rings with the ...
Laššák, Miroslav, Porubský, Štefan
core   +1 more source

Gr\"obner Bases over Algebraic Number Fields

, 2015
Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field.
Boku, Dereje Kifle, Decker, Wolfram, Fieker, Claus, Steenpass, Andreas   +3 more
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Splitting full matrix algebras over algebraic number fields

, 2011
Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n.
Acciaro, Babai, Bremner, Buchmann, Cassels, Chistov, Cohen, Cremona, Cremona, Cremona, Cremona, de Graaf, de Graaf, Eberly, Eberly, Eberly, Eberly, Fisher, Gábor Ivanyos, Hollanti, Ivanyos, Ivanyos, Ivanyos, Ivanyos, Ivanyos, Jacobson, Janusz, Josef Schicho, Kannan, Lajos Rónyai, Lenstra, Lenstra, Matoušek, Nebe, Pan, Pierce, Pílniková, Reiner, Rónyai, Rónyai, Rónyai, Rónyai, Sethuraman, Simon   +43 more
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Algorithms in algebraic number theory [PDF]

, 1992
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and,
Lenstra Jr., Hendrik W.
core   +5 more sources

Elementary Fractal Geometry. 2. Carpets Involving Irrational Rotations

Fractal and Fractional, 2022
Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles.
Christoph Bandt, Dmitry Mekhontsev
doaj   +1 more source

Analytic curves in algebraic varieties over number fields

, 2007
We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'
A Franchetta, B Dwork, C P Ramanujam, D G Cantor, D Harbater, D Mumford, D V Chudnovsky, D V Chudnovsky, E Kani, G Eisenstein, G Pólya, H Hironaka, H Hironaka, H Matsumura, H Randriambololona, J Fresnel, J.-B. Bost, J.-B. Bost, J.-B. Bost, J.-B. Bost, J.-P. Serre, L Bădescu, L Moret-Bailly, L Moret-Bailly, M Raynaud, M van der Put, P Graftieaux, P Graftieaux, R Hartshorne, R Hartshorne, R Rumely, R S Rumely, S Bosch, S Bosch, S Bosch, V G Berkovich, W Gubler, Y Amice, Y André, Y Ihara, Yu. I. Manin, É Borel   +41 more
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The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings

Entropy, 2021
Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring ...
Jheyne N. Ortiz, Robson R. de Araujo, Diego F. Aranha, Sueli I. R. Costa, Ricardo Dahab   +4 more
doaj   +1 more source

Generalised Mertens and Brauer-Siegel Theorems [PDF]

, 2007
In this article, we prove a generalisation of the Mertens theorem for prime numbers to number fields and algebraic varieties over finite fields, paying attention to the genus of the field (or the Betti numbers of the variety), in order to make it tend to
Brauer-siegel Theorems <, Generalised Mertens, Hal Id Hal, Philippe Lebacque   +3 more
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