TY - JOUR
ID - 13745
TI - Classification of rings with toroidal annihilating-ideal graph
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Krishnan, Selvakumar
AU - P, Subbulakshmi
AD - Department of Mathematics
Manonmaniam Sundaranar University
Tirunelveli
AD - Manonmaniam Sundaranar University
Y1 - 2018
PY - 2018
VL - 3
IS - 2
SP - 93
EP - 119
KW - annihilating-ideal
KW - planar
KW - genus
KW - local ring
KW - annihilating-ideal graph
DO - 10.22049/cco.2018.26060.1072
N2 - Let $R$ be a non-domain commutative ring with identity and $A^*(R)$ be the set of non-zero ideals with non-zero annihilators. We call an ideal $I$ of $R$, an annihilating-ideal if there exists a non-zero ideal $J$ of $R$ such that $IJ =(0)$. The annihilating-ideal graph of $R$ is defined as the graph $AG(R)$ with the vertex set $A^*(R)$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ =(0)$. In this paper, we characterize all commutative Artinian nonlocal rings $R$ for which $AG(R)$ has genus one.
UR - http://comb-opt.azaruniv.ac.ir/article_13745.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13745_64b16e21db453555d1fe39afe192d7e5.pdf
ER -