In this paper we introduce and study the spectrum graph of a commutative ring R, denoted
by 𝔸𝔾s (R), that is, the graph whose vertices are all non-zero prime ideals of R with non …

A GRAPH ASSOCIATED TO SPECTRUM OF A COMMUTATIVE RING 1. Introduction
Throughout this paper all rings are commutative with non-ze Page 1 Journal of Algebra and …

The rings considered in this article are commutative rings with identity $1\neq 0$. The aim of
this article is to define and study the exact annihilating-ideal graph of commutative rings. We …

Let R be a commutative ring with identity and A*(R) be the set of non-zero ideals with non-
zero annihilators. The annihilatingideal graph of R is defined as the graph AG (R) with the …

Let R be a commutative ring with identity and 𝔸 (R) be the set of ideals of R with nonzero
annihilator. The annihilator-ideal graph of R, denoted by AI (R), is a simple graph with the …

Let R be a commutative ring with A⁢(R) its set of annihilating-ideals. The extended
annihilating-ideal graph of R, denoted by AG¯⁢(R), is an undirected graph with vertex set …

The Co-annihilating-ideal Graphs of Commutative Rings Page 1 Canad. Math. Bull. Vol. ( ),
pp. – http://dx.doi.org/. /CMB--©Canadian Mathematical Society The Co-annihilating-ideal …

Let R be a commutative ring with unity, A (R) be the set of all annihilating-ideals of R and
A∗(R)= A (R)\{0}. In this paper, we introduced and studied the essential annihilating-ideal …

Let R be a commutative ring with identity and A∗(R) be the set of non-zero ideals with non-
zero annihilators. The annihilating-ideal graph of R is defined as the graph AG (R) with the …

Let $ R $ be a commutative ring with identity, and let $ Z (R) $ be the set of zero-divisors of $
R $. The annihilator graph of $ R $ is defined as the undirected graph $ AG (R) $ with the …