Let $R$ be a commutative ring and let $\Bbb A(R)$ be the 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 two distinct 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.
Adlifard, M., & Payrovi, S. (2021). Some classes of perfect annihilator-ideal graphs associated with commutative rings. Journal of Algebra and Related Topics, 9(1), 21-29. doi: 10.22124/jart.2021.17227.1214
MLA
M. Adlifard; Sh. Payrovi. "Some classes of perfect annihilator-ideal graphs associated with commutative rings". Journal of Algebra and Related Topics, 9, 1, 2021, 21-29. doi: 10.22124/jart.2021.17227.1214
HARVARD
Adlifard, M., Payrovi, S. (2021). 'Some classes of perfect annihilator-ideal graphs associated with commutative rings', Journal of Algebra and Related Topics, 9(1), pp. 21-29. doi: 10.22124/jart.2021.17227.1214
VANCOUVER
Adlifard, M., Payrovi, S. Some classes of perfect annihilator-ideal graphs associated with commutative rings. Journal of Algebra and Related Topics, 2021; 9(1): 21-29. doi: 10.22124/jart.2021.17227.1214
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