TY - JOUR
ID - 4805
TI - Some classes of perfect annihilator-ideal graphs associated with commutative rings
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Adlifard, M.
AU - Payrovi, Sh.
AD - Department of Mathematics, Roudbar Branch Islamic Azad University, Roudbar, Iran
AD - Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
Y1 - 2021
PY - 2021
VL - 9
IS - 1
SP - 21
EP - 29
KW - Annihilator-ideal graph
KW - Perfect graph
KW - Chromatic number
KW - Clique number
DO - 10.22124/jart.2021.17227.1214
N2 - Let $R$ be a commutative ring and let $\Bbb A(R)$ bethe set of all ideals of $R$ with nonzero annihilator.The annihilator-ideal graph of $R$ is defined as the graph${A_I}(R)$ with the vertex set $\Bbb A(R)^*=\Bbb A(R)\setminus\{0\}$ and twodistinct vertices $I$ and $J$ are adjacent if and only if${\rm Ann}_R(IJ)\neq{\rm Ann}_R(I) \cup{\rm Ann}_R(J)$. In this paper, perfectness of${A_I}(R)$ for some classes of rings is investigated.
UR - https://jart.guilan.ac.ir/article_4805.html
L1 - https://jart.guilan.ac.ir/article_4805_94dd66e60e677c95c058bec639a9936b.pdf
ER -