The rings considered in this article are commutative with identity which admit at least two maximal ideals. Let $R$ be a ring such that $R$ admits at least two maximal ideals. Recall from Ye and Wu (J. Algebra Appl. 11(6): 1250114, 2012) that the comaximal ideal graph of $R$, denoted by $\mathscr{C}(R)$ is an undirected simple graph whose vertex set is the set of all proper ideals $I$ of $R$ such that $I\not\subseteq J(R)$, where $J(R)$ is the Jacobson radical of $R$ and distinct vertices $I_{1}$, $I_{2}$ are joined by an edge in $\mathscr{C}(R)$ if and only if $I_{1} + I_{2} = R$. In Section 2 of this article, we classify rings $R$ such that $\mathscr{C}(R)$ is planar. In Section 3 of this article, we classify rings $R$ such that $\mathscr...
summary:Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and st...
Let R be a commutative ring and I be a non-zero ideal of R. Let R⋈I be the subring of R×R consisting...
summary:Let $R$ be a commutative ring with unity and $U(R)$ be the set of unit elements of $R$. In t...
The rings considered in this article are commutative with identity which admit at least two maximal ...
The rings considered in this article are commutative with identity which admit at least two maximal ...
The rings considered in this article are commutative with identity which admit at least two maximal ...
Let $R$ be a commutative ring with unity. The comaximal ideal graph of $R$, denoted by $mathcal{C}(R...
Let R R be a commutative ring with unity. The comaximal ideal graph of R R, denoted by C(R) C(R), is...
AbstractLet R be a commutative ring R with 1. In [P.K. Sharma, S.M. Bhatwadekar, A note on graphical...
Let R be a commutative ring with identity 1 ̸= 0. Define the comaximal graph of R, denoted by CG(R),...
In this paper we introduce a new kind of graph associated with a commutative ring with identity, and...
Let R be a commutative ring with nonzero identity, and let I be an ideal of R. The ideal-based zero-...
Let R be a commutative ring. We associate a digraph to the ideals of R whose vertex set is the set o...
summary:Let $R$ be a commutative ring with identity and $A(R)$ be the set of ideals with nonzero ann...
AbstractLet R be a commutative ring with identity. Let A(R) denote the collection of all annihilatin...
summary:Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and st...
Let R be a commutative ring and I be a non-zero ideal of R. Let R⋈I be the subring of R×R consisting...
summary:Let $R$ be a commutative ring with unity and $U(R)$ be the set of unit elements of $R$. In t...
The rings considered in this article are commutative with identity which admit at least two maximal ...
The rings considered in this article are commutative with identity which admit at least two maximal ...
The rings considered in this article are commutative with identity which admit at least two maximal ...
Let $R$ be a commutative ring with unity. The comaximal ideal graph of $R$, denoted by $mathcal{C}(R...
Let R R be a commutative ring with unity. The comaximal ideal graph of R R, denoted by C(R) C(R), is...
AbstractLet R be a commutative ring R with 1. In [P.K. Sharma, S.M. Bhatwadekar, A note on graphical...
Let R be a commutative ring with identity 1 ̸= 0. Define the comaximal graph of R, denoted by CG(R),...
In this paper we introduce a new kind of graph associated with a commutative ring with identity, and...
Let R be a commutative ring with nonzero identity, and let I be an ideal of R. The ideal-based zero-...
Let R be a commutative ring. We associate a digraph to the ideals of R whose vertex set is the set o...
summary:Let $R$ be a commutative ring with identity and $A(R)$ be the set of ideals with nonzero ann...
AbstractLet R be a commutative ring with identity. Let A(R) denote the collection of all annihilatin...
summary:Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and st...
Let R be a commutative ring and I be a non-zero ideal of R. Let R⋈I be the subring of R×R consisting...
summary:Let $R$ be a commutative ring with unity and $U(R)$ be the set of unit elements of $R$. In t...