TY - JOUR
ID - 3328
TI - Some results on a subgraph of the intersection graph of ideals of a commutative ring
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Visweswaran, S.
AU - Vadhel, P.
AD - Department of Mathematics,
Saurashtra University, Rajkot, India.
AD - Department of Mathematics,
Saurashtra University, Rajkot, India
Y1 - 2018
PY - 2018
VL - 6
IS - 2
SP - 35
EP - 61
KW - Artinian ring
KW - Special principal ideal ring
KW - diameter
KW - girth
KW - clique number
DO - 10.22124/jart.2018.11188.1114
N2 - The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal. Let $R$ be a ring. Let us denote the collection of all proper ideals of $R$ by $mathbb{I}(R)$ and $mathbb{I}(R)backslash {(0)}$ by $mathbb{I}(R)^{*}$. With $R$, we associate an undirected graph denoted by $g(R)$, whose vertex set is $mathbb{I}(R)^{*}$ and distinct vertices $I_{1}, I_{2}$ are adjacent in $g(R)$ if and only if $I_{1}cap I_{2}neq I_{1}I_{2}$. The aim of this article is to study the interplay between the graph-theoretic properties of $g(R)$ and the ring-theoretic properties of $R$.
UR - https://jart.guilan.ac.ir/article_3328.html
L1 - https://jart.guilan.ac.ir/article_3328_37da989245b3ff3ca164523e990de30b.pdf
ER -