Add to ORKGThe digraphs of commutative rings under modular arithmetic reveal intriguing cycle patterns, many of which have yet to be explained. To help illuminate these patterns, we establish a set of new theorems. Rings with relatively prime moduli a and b are used to predict cycles in the digraph of the ring with modulus ab. Rings that use Pythagorean primes as their modulus are shown to always have a cycle in common. Rings with perfect square moduli have cycles that relate to their square root
AbstractThe commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non-cent...
summary:For a finite commutative ring $R$ and a positive integer $k\geqslant 2$, we construct an ite...
summary:We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set o...
summary:The paper extends the results given by M. Křížek and L. Somer, {\it On a connection of numbe...
The directed graph of a commutative ring is a graph representation of its additive and multiplicativ...
In this paper, we examine the algebraic properties of localizations of commutative rings and how lo...
summary:We assign to each positive integer $n$ a digraph whose set of vertices is $H=\lbrace 0,1,\do...
AbstractWe assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,…,n-1} a...
Various graphs associated with a commutative (non commutative) ring are presented. This presentation...
A result of Herstein says in particular that if there exists n > 1 such that xᵑ − x ∈ Z(R) for all ...
Abstract: A commutative rings’ additive and multiplicative structure can be represented with a direc...
AbstractWe say that a digraph is essentially cyclic if its Laplacian spectrum is not completely real...
For a commutative ring R with unity, the associate ring graph, denoted by AG(R), is a simple graph w...
summary:In the first part, we assign to each positive integer $n$ a digraph $\Gamma (n,5),$ whose se...
The directed graph of a ring is a graphical representation of its additive and multiplicative struct...
AbstractThe commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non-cent...
summary:For a finite commutative ring $R$ and a positive integer $k\geqslant 2$, we construct an ite...
summary:We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set o...
summary:The paper extends the results given by M. Křížek and L. Somer, {\it On a connection of numbe...
The directed graph of a commutative ring is a graph representation of its additive and multiplicativ...
In this paper, we examine the algebraic properties of localizations of commutative rings and how lo...
summary:We assign to each positive integer $n$ a digraph whose set of vertices is $H=\lbrace 0,1,\do...
AbstractWe assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,…,n-1} a...
Various graphs associated with a commutative (non commutative) ring are presented. This presentation...
A result of Herstein says in particular that if there exists n > 1 such that xᵑ − x ∈ Z(R) for all ...
Abstract: A commutative rings’ additive and multiplicative structure can be represented with a direc...
AbstractWe say that a digraph is essentially cyclic if its Laplacian spectrum is not completely real...
For a commutative ring R with unity, the associate ring graph, denoted by AG(R), is a simple graph w...
summary:In the first part, we assign to each positive integer $n$ a digraph $\Gamma (n,5),$ whose se...
The directed graph of a ring is a graphical representation of its additive and multiplicative struct...
AbstractThe commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non-cent...
summary:For a finite commutative ring $R$ and a positive integer $k\geqslant 2$, we construct an ite...
summary:We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set o...