Anirudhdha Parmar
Saurashtra University
[ 1 ] - Some results on the complement of a new graph associated to a commutative ring
The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal. Let $R$ be a ring. We denote the collection of all ideals of $R$ by $\mathbb{I}(R)$ and $\mathbb{I}(R)\backslash \{(0)\}$ by $\mathbb{I}(R)^{*}$. Alilou et al. [A. Alilou, J. Amjadi and S.M. Sheikholeslami, {\em A new graph associated to a commutative ring}, Discrete Math. Algorithm. …
[ 2 ] - Line graphs associated to the maximal graph
Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $\Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphic…
[ 3 ] - A note on maximal non-prime ideals
The rings considered in this article are commutative with identity $1\neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $I\neq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ I\subseteq A$ and $I\neq A$ is a prime ideal. That is, among all the proper ideals of $R$, …
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