Randomized trial investigates perfectness of annihilator graph in Artinian rings, highlighting its structural properties.
Let R be a commutative ring and $Z(R)$ be the set of its zero-divisors.The annihilator graph of R, denoted by $AG(R)$ is a simple undirected graph whose vertexset is Z(R)^*, the set of all nonzero zero-divisors of R, and two distinct vertices x andy are adjacent if and only if annR(xy)≠ annR(x)∪ annR(y).In this paper, perfectness of the annihilator graph for some classes of rings is investigated.More precisely, we show that if R is an Artinian ring, then $AG(R)$ is perfect.
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Adlifard et al. (2023) studied this question.
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