We associate an undirected graph Γf (M) to M in which non-zero elements x and y of M are
adjacent provided that xf (y)= 0 or yf (x)= 0. We observe that over a commutative ring R, Γf …

Let R be a commutative ring and A (R) be the set of all ideals with non-zero annihilators.
Assume that A∗(R)= A (R)⧹{(0)} and F (R) denote the set of all finitely generated ideals of R …

Let R be a commutative ring with identity and Z (R) be its set of zerodivisors. The study of
coloring of zero-divisor graphs of commutative rings dates back to [3]. For the information …

Let R be a commutative ring with identity. The main purpose of this paper is to introduce the
notions of comultiplication-like and virtually codivisible R-modules as generalizations of …

Let $ M $ be a module over a commutative ring $ R $, $ Z_ {*}(M) $ be its set of weak zero-
divisor elements, andif $ m\in M $, then let $ I_m=(Rm: _R M)=\{r\in R: rM\subseteq Rm\} …

Let R be a commutative ring and M be an R-module, if x∈ M, Ix:={r∈ R| rM⊆ Rx} and ann
(IxM={r∈ R| rIxM= 0}. The annihilator graph of module M over ring R is the graph AG (RM) …

For a finite group $ G $, the proper power graph $\mathscr {P}^*(G) $ of $ G $ is the graph
whose vertices are non-trivial elements of $ G $ and two vertices $ u $ and $ v $ are …

In this paper, using module endomorphisms, we extend the concept of the zero-divisor
graph of a ring to a module over an arbitrary commutative ring. The main aim of this article is …

Let $ R $ be a commutative ring with nonzero identity and let $ M $ be a unitary $ R $-
module. The essential graph of $ M $, denoted by $ EG (M) $ is a simple undirected graph …

Let R be a commutative ring with a non-zero identity. In this paper, we define a new graph,
the compressed intersection annihilator graph, denoted by $ IA (R) $, and investigate some …