TY - JOUR ID - 2728 TI - Some Remarks on $(\operatorname{INC}(R))^{c}$ JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Purohit, Krishna L AU - Parejiya, Jaydeep AU - Parsania, Mahesh M AD - Department of Applied Sciences, RK University, Rajkot-360020, Gujarat, India. AD - Department of Mathematics, Government Polytechnic, Rajkot-360003, Gujarat, India. Y1 - 2022 PY - 2022 VL - 9 IS - 2 SP - 181 EP - 198 KW - $(operatorname{INC}(R))^{c}$ KW - Maximal ideal, SPIR DO - 10.22034/as.2022.2728 N2 - Let $R$ be a commutative ring with identity $1 \neq 0$ which admits atleast 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 $(\operatorname{INC}(R))^{c}$. UR - https://as.yazd.ac.ir/article_2728.html L1 - https://as.yazd.ac.ir/article_2728_f39a6f6a24600b29ee4c547dbc9f4923.pdf ER -