In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

Let R be a commutative ring with Z∗(R) as the set of nonzero zero divisors. The zero divisor
graph of R, denoted by Γ (R), is the graph whose vertex set is Z∗(R), where two distinct …

Let M be an R-module, where R is a commutative ring with identity 1 and let G (V, E) be a
graph. In this paper, we study the graphs associated with modules over commutative rings …

In this paper, we will extend the notion of zero-divisor graph of commutative rings to zero-
divisor graph of abelian groups and study this zero-divisor graph. We characterize the zero …

Let $ R $ be a ring and $ M $ be an $ R $-module. Two modules $ A $ and $ B $ are called
orthogonal, written $ A\perp B $, if they do not have non-zero isomorphic submodules. We …

On the strongly annihilating-submodule graph of a module Page 1 Hacettepe Journal of
Mathematics & Statistics Hacet. J. Math. Stat. Volume 51 (2) (2022), 443 – 454 DOI …

Abstract Consider $ M_n (\mathbf {Z} _p) $, the matrix ring of order $ n $ over the field
$\mathbf {Z} _p $. In this paper, we deduce a relation to find the number of zero divisors in …

Let R be a commutative ring and M a Noetherian R-module. The zero-divisor graph of M,
denoted by Γ (M), is an undirected simple graph whose vertices are the elements of ZR …

A Generalization of Torsion Graph for Modules Login Login 切换导航 Home Articles Journals
Books News About Services Submit Home Journals Article Applied Mathematics > Vol.15 …

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a
graph to M, sayΓ (RM), such that when M= R, Γ (RM) coincide with the zero-divisor graph of …