«Annihilating-ideal»
۴۷۸ نتیجهSome results on the strongly annihilator ideal graph of a lattice
For a lattice $L$, the strongly annihilator ideal graph of $L$ is denoted by $SAnnIG(L)$. It is a graph with the vertex set, which consists of all ideals in $L$ that have nontrivial annihilators such that any two distinct vertices $I$ and $J$ are adjacent in $SAnnIG(L)$ if and on
Characterization of zero-dimensional rings such that the clique number of their annihilating-ideal graphs is at most four
The rings considered in this article are commutative with identity which are not integral domains. Let $R$ be a ring. An ideal $I$ of $R$ is said to be an annihilating ideal of $R$ if there exists $r\in R\backslash \{0\}$ such that $Ir = (0)$. Let $\mathbb{A}(R)$ denote the set o
Classification of rings with toroidal annihilating-ideal graph
Let $R$ be a non-domain commutative ring with identity and $A^*(R)$ be the set of non-zero ideals with non-zero annihilators. We call an ideal $I$ of $R$, an annihilating-ideal if there exists a non-zero ideal $J$ of $R$ such that $IJ =(0)$. The annihilating-ideal graph of $R$ is
The strongly annihilating-ideal graph of a commutative ring with respect to an ideal
For a commutative ring $R$ with identity, ${\rm SAG}(R)$ be the graph whose vertices are the nonzero annihilating ideals of $R$ and with two distinct nonzero annihilating ideals $I$ and $J$ joined by an edge when $I\cap {\rm Ann}(J)\neq (0)$ and $J\cap {\rm Ann}(I) \neq (0)$. Als
Exact annihilating-ideal graph of commutative rings
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 discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic
the principal ideal subgraph of the annihilating-ideal graph of commutative rings
let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (und
The principal ideal subgraph of the annihilating-ideal graph of commutative rings
Let $R$ be a commutative ring with identity and $\mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $\mathbb{AG}_P(R)$. It is a (u
Some Remarks on the Annihilating-Ideal Graph of Commutative Ring with Respect to an Ideal
The graph $ AG ( R ) $ {of} a commutative ring $R$ with identity has an edge linking two unique vertices when the product of the vertices equals {the} zero ideal and its vertices are the nonzero annihilating ideals of $R$.The annihilating-ideal graph with {respect to} an ideal $
when does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?
the rings considered in this article are commutative with identity which admit at least two nonzero annihilating ideals. let $r$ be a ring. let $mathbb{a}(r)$ denote the set of all annihilating ideals of $r$ and let $mathbb{a}(r)^{*} = mathbb{a}(r)backslash {(0)}$. the annihilati
Some properties of the essential annihilating-ideal graph of commutative rings
Let $\mathcal{S}$ be a commutative ring with unity and $A(\mathcal{S})$ denotes the set of annihilating-ideals of $\mathcal{S}$. The essential annihilating-ideal graph of $\mathcal{S}$, denoted by $\mathcal{EG}(\mathcal{S})$, is an undirected graph with $A^*(\mathcal{S})$ as the