Results 1 to 10 of about 1,605,092 (298)

Enumeration of Involutions of Finite Rings

Journal of New Theory, 2021
In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution of a ring R is an element with the property that x^2-1=0 for some x in R.
Sajana Shaık, Chalapathi Tekurı
doaj   +1 more source

Rings of Multisets and Integer Multinumbers

Mathematics, 2022
In the paper, we consider a ring structure on the Cartesian product of two sets of integer multisets. In this way, we introduce a ring of integer multinumbers as a quotient of the Cartesian product with respect to a natural equivalence.
Yuriy Chopyuk, Taras Vasylyshyn, Andriy Zagorodnyuk   +2 more
doaj   +1 more source

Free products of cyclic groups in groups of infinite unitriangular matrices

Математичні Студії, 2023
Groups of infinite unitriangular matrices over associative unitary rings are considered. These  groups naturally act on infinite dimensional free modules over underlying rings. They are profinite in case underlying rings are finite.
A. Oliynyk
doaj   +1 more source

Theory on Duplicity of Finite Neutrosophic Rings [PDF]

Neutrosophic Sets and Systems, 2023
This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic rings. The authors establish duplex ring and neutrosophic duplex ring by way of various illustrations.
T. Chalapathi, K. Kumaraswamy Naidu, D. Harish Babu, Florentin Smarandache   +3 more
doaj   +1 more source

The Mathematical Safe Problem and Its Solution (Part 2)

Кібернетика та комп'ютерні технології, 2021
Introduction. The problem of mathematical safe arises in the theory of computer games and cryptographic applications. The article considers numerous variations of the mathematical safe problem and examples of its solution using systems of linear ...
Sergii Kryvyi, Hryhorii Hoherchak
doaj   +1 more source

The Mathematical Safe Problem and Its Solution (Part 1)

Кібернетика та комп'ютерні технології, 2020
Introduction. The problem of the mathematical safe arises in the theory of computer games and cryptographic applications. The article considers the formulation of the mathematical safe problem and the approach to its solution using systems of linear ...
S. Kryvyi, H. Hoherchak
doaj   +1 more source

On r-Noncommuting Graph of Finite Rings

Axioms, 2021
Let R be a finite ring and r∈R. The r-noncommuting graph of R, denoted by ΓRr, is a simple undirected graph whose vertex set is R and two vertices x and y are adjacent if and only if [x,y]≠r and [x,y]≠−r.
Rajat Kanti Nath, Monalisha Sharma, Parama Dutta, Yilun Shang   +3 more
doaj   +1 more source

Linear codes and cyclic codes over finite rings and their generalizations: a survey

Electronic Journal of Graph Theory and Applications, 2023
We survey a recent progress of cyclic codes over finite rings and their generalization to skew cyclic as well as skew cyclic codes with derivation over finite rings, focusing on structural properties of the codes.
Djoko Suprijanto
doaj   +1 more source

LAPLACIAN SPECTRUM AND ENERGY OF NON-COMMUTING GRAPHS OF FINITE RINGS [PDF]

Journal of Algebraic Systems
We compute spectrum, energy, Laplacian spectrum/ energy and signless Laplacian spectrum/energy of non-commuting graphs of certain finite non-commutative rings. In particular, we consider finite rings $R$ such that $|R| = p^2, p^3, p^4$, $p^5$, $p^2q$ and
Monalisha Sharma, Rajat Nath
doaj   +1 more source

A commutativity‐or‐finiteness condition for rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2004
We show that a ring with only finitely many noncentral subrings must be either commutative or finite.
Abraham A. Klein, Howard E. Bell
openaire   +3 more sources