Results 31 to 40 of about 5,453 (309)

Unit and Unitary Cayley Graphs for the Ring of Eisenstein Integers Modulo N [PDF]

, 2021
Let En be the ring of Eisenstein integers modulo n. We denote by G(En) and GEn, the unit graph and the unitary Cayley graph of En, respectively. In this paper, we obtain the value of the diameter, the girth, the clique number and the chromatic number of ...
Bahrami, A., Jahani-Nezhad, R.
core   +1 more source

Additive Hilbert's Theorem 90 in the ring of algebraic integers [PDF]

, 2006
For a number field K, we give a complete characterization of algebraic numbers which can be expressed by a difference of two K-conjugate algebraic integers.
Dubickas, Artūras, Artūras Dubickas
core   +1 more source

Chinese remainder theorem secret sharing in multivariate polynomials

Журнал Белорусского государственного университета: Математика, информатика, 2019
This paper deals with a generalization of the secret sharing using Chinese remainder theorem over the integers to multivariate polynomials over a finite field. We work with the ideals and their Gröbner bases instead of integer moduli.
Gennadii V. Matveev
doaj   +1 more source

Algebraic relations among Goss’s zeta values on elliptic curves

Forum of Mathematics, Sigma, 2023
In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for $A=\mathbb F_q[\theta ]$ , also known as the Carlitz zeta values.
Nathan Green, Tuan Ngo Dac
doaj   +1 more source

Construction of Complex Lattice Codes via Cyclotomic Fields

Trends in Computational and Applied Mathematics, 2022
Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized ...
E. D. Carvalho, A. A. Andrade, T. Shah, C. C. Trinca   +3 more
doaj   +1 more source

A ring of Gaussian integers and applications [PDF]

, 2020
Prsten Gaussovih cijelih brojeva \(\mathbb{Z} [i]\)generalizacija je prstena cijelih brojeva \(\mathbb{Z}\). Kao takvi, Gaussovi cijeli brojevi zadržali su većinu svojstava cijelih brojeva.
Novak, Iva
core  

On the decidability of the theory of modules over the ring of algebraic integers [PDF]

, 2017
We will prove that the theory of all modules over the ring of algebraic integers is ...
TOFFALORI, Carlo, Carlo Toffalori, Sonia L'Innocente, Gena Puninski, L'INNOCENTE, Sonia, Puninski, Gena   +5 more
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The Diophantine equation ax2+2bxy−4ay2=±1

International Journal of Mathematics and Mathematical Sciences, 2003
We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers.
Lionel Bapoungué
doaj   +1 more source

Ergodic dynamical systems over the cartesian power of the ring of p-adic integers [PDF]

, 2014
International audienceV. Anashin gave criteria for measure-preservation and ergodicity of 1-lipschitz transformations on the ring of p-adic integers. Most recently V.
Sopin, Valerii
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On Generation of the Group $PGL_n(\mathbb{Z}+i\mathbb{Z})$ by Three Involutions, Two of which Commute

Известия Иркутского государственного университета: Серия "Математика"
The results of the paper relate to the following general problem. Find natural finite generating  sets of elements of a given linear group over a finitely generated commutative ring.
Ya.N. Nuzhin, T. B. Shaipova
doaj   +1 more source