Results 1 to 10 of about 1,202 (263)
On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics, 2021 In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda +2 more
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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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K2 of rings of algebraic integers
Journal of Number Theory, 1992 For a number field \(F\) and a prime number \(p\), the author studies \(K_ 2{\mathcal O}_ F\otimes\mathbb{Z}_ p\) as a module of Iwasawa descent. The paper consists of two parts: 1) Let \(G_ \infty=\text{Gal}\bigl(F(\mu_{p^ \infty})/F\bigr)\), \(U_ \infty=\) the group of units of \(F\bigl(\mu_{p^ \infty}\bigr)\), \(A_ \infty=\) the \(p\)-class group of
exaly +3 more sources
Springer Proceedings in Mathematics and StatisticsLet F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of Int(O_K) modulo a non-zero prime ideal is GE2 (meaning that every unimodular pair can be trasformed to (1,0) by a series ...
Sophie Frisch +2 more
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A Review Study on Some Properties of The Structure of Neutrosophic Ring [PDF]
Neutrosophic Sets and Systems, 2023 In this article we use neutrosophy to introduced Particular Structure of neutrosophic ring and studied some theorem and properties according to classical axiomatic ring theory.
Adel Al-Odhari
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Solutions of Some Kandasamy-Smarandache Open Problems About the Algebraic Structure of Neutrosophic Complex Finite Numbers [PDF]
Neutrosophic Sets and Systems, 2023 The aim of this paper is to study the neutrosophic complex finite rings 𝐶(𝑍𝑛 ) 𝑎𝑛𝑑 𝐶(< 𝑍𝑛 ∪ 𝐼 >), and to give a classification theorem of these rings. Also, this work introduces full solutions for 12 Kandasamy-Smarandache open problems concerning these ...
Basheer Abd Al Rida Sadiq
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Montgomery Reduction for Gaussian Integers
Cryptography, 2021 Modular arithmetic over integers is required for many cryptography systems. Montgomery reduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Montgomery reduction is used for rings of ordinary integers.
Malek Safieh, Jürgen Freudenberger
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On graphs associated to ring of Guassian integers and ring of integers modulo n
Acta Universitatis Sapientiae, Informatica, 2022 Abstract For a commutative ring R with identity 1, the zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is the set of non-zero zero divisors Z*(R) and the two vertices x and y ∈ Z*(R) are adjacent if and only if xy = 0.
Pirzada S., Bhat M. Imran
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On the size of Diophantine m-tuples in imaginary quadratic number rings
Bulletin of Mathematical Sciences, 2021 A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers.
Nikola Adžaga
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On distribution of the number of semisimple rings of order at most x in an arithmetic progression [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let ℓ and q denote relatively prime positive integers. In this article, we derive the asymptotic formula for the summation Σ_{n≤x, n≡ℓ (mod q)} S(n), where S(n) denotes the number of non-isomorphic finite semisimple rings with n elements.
Thorranin Thansri +2 more
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