Some Remarks on $(\operatorname{INC}(R))^{c}$

Document Type : Research Paper

Authors

1 Department of Applied Sciences, RK University, Rajkot-360020, Gujarat, India.

2 Department of Mathematics, Government Polytechnic, Rajkot-360003, Gujarat, India.

10.29252/as.2022.2728

Abstract

Let $R$ be a commutative ring with identity $1 \neq 0$ which admits at least two maximal ideals. In this article, we have studied simple, undirected graph $(\operatorname{INC}(R))^{c}$ whose vertex set is the set of all proper ideals which are not contained in $J(R)$ and two distinct vertices $I_{1}$ and $I_{2}$ are joined by an edge in $(\operatorname{INC}(R))^{c}$ if and only if $I_{1} \subseteq I_{2}$ or $I_{2} \subseteq I_{1}$. In this article, we have studied some interesting properties of $(\operatorname{INC}(R))^{c}$.

Keywords


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