Results 1 to 10 of about 798 (168)

A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]

Heliyon
This 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, Hafiz Muhammad Afzal Siddiqui, Muhammad Bilal Riaz, Muhammad Imran Qureshi, Ali Akgül   +4 more
doaj   +2 more sources

An Introduction to i-Commutative Rings

Mathematics
In this paper, we introduce a new class of rings, called i-commutative rings, by extending the concept of commutative-like rings using idempotent elements.
Muhammad Saad, Usama A Aburawash, A M A El-Sayed   +2 more
exaly   +3 more sources

NeutroAlgebra of Idempotents in Group Rings [PDF]

Neutrosophic Sets and Systems, 2022
In this paper, the authors study the new concept of NeutroAlgebra of idempotents in group rings. It is assumed that RG is the group ring of a group G over the ring R. R should be a commutative ring with unit 1.
Vasantha Kandasamy, Ilanthenral Kandasamy   +1 more
doaj   +1 more source

On the Genus of the Idempotent Graph of a Finite Commutative Ring

Discussiones Mathematicae - General Algebra and Applications, 2021
Let R be a finite commutative ring with identity. The idempotent graph of R is the simple undirected graph I(R) with vertex set, the set of all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = 0.
Belsi G. Gold, Kavitha S., Selvakumar K.
doaj   +1 more source

Reticulation of Quasi-commutative Algebras [PDF]

Journal of Mahani Mathematical Research, 2023
The commutator theory, developed by Fresee and McKenzie in the framework of a congruence-modular variety $\mathcal{V}$, allows us to define the prime congruences of any algebra $A\in \mathcal{V}$ and the prime spectrum $Spec(A)$ of $A$.
G. Georgescu
doaj   +1 more source

Centrally Prime Rings which are Commutative [PDF]

Kirkuk Journal of Science, 2006
In this paper the definition of centrally prime rings is introduced , our main purpose is to classify those centrally prime rings which are commutative and so that several conditions are given each of which makes a centrally prime ring commutative.
Adil K.Jabbar
doaj   +1 more source

Commutative periodic group rings

Математичні Студії, 2020
We find a satisfactory criterion when a commutative group ring $R(G)$ is periodic only in terms of $R$, $G$ and their sections, provided that $R$ is local.
P. Danchev
doaj   +1 more source

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

On Commutative Gelfand Rings

, 2021
By studying and using the quasi-pure part concept, we improve some statements and show that some assumptions in some articlesare superfluous. We give some characterizations of Gelfand rings. For example: we prove that R is Gelfand if and only if m(∑ α∈A Iα) =∑α∈A m(Iα), for each family {Iα}α∈A of ideals of R, in addition if R is semiprimitive and Max(R)
Badie, Mehdi, Nazari, Sajad, Aliabad, Ali Rezaei   +2 more
openaire   +3 more sources

A NON-COMMUTATIVE GENERALIZATION OF MTL-RINGS [PDF]

Journal of Algebraic Systems
The current work extends the class of commutative MTL-rings established by the authors to the non-commutative ones. That class of rings will be named generalized MTL-rings since they are not necessary commutative. We show that in the non-commutative case,
Samuel Mouchili, Surdive Atamewoue, Selestin Ndjeya   +2 more
doaj   +1 more source