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. In this paper, we study the annihilatorideal-based zero-divisor
graph by replacing the ideal I of R with the idealAnnR (M) for an R-module M. Also, we …

Let R be a commutative ring with identity, and let M be an R-module. In this paper, we focus
on the ideals of R that are annihilators of torsion elements of M. In analogy with definitions …

Let R be a commutative ring with identity. Let M be an R-module and T (M)* be the set of
nonzero torsion elements. The set T (M)* makes up the vertices of the corresponding torsion …

Let 𝑅 be a commutative ring with identity. Let 𝑀 be an 𝑅-module and 𝑇 (𝑀)* be the set of
nonzero torsion elements. The set 𝑇 (𝑀)* makes up the vertices of the corresponding torsion …

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 …

arXiv:1610.05042v1 [math.AC] 17 Oct 2016 Page 1 arXiv:1610.05042v1 [math.AC] 17 Oct 2016
AN IDEAL-BASED COZERO-DIVISOR GRAPH OF A COMMUTATIVE RING H …

When David F. Anderson retired in September 2017, his many friends and colleagues from
around the world felt it appropriate to acknowledge his contributions to the wide-ranging …

Let X be a quasi-compact scheme and x∈ X. By cp (X) and cl (x), we denote the set of
closed points of X and the closure of the subset {x}. Let S be a nonempty subset of cp (X) …

Beck's conjecture on coloring of graphs associated to various algebraic objects has
generated considerable interest in the community of discrete mathematics and …