Geodesic
Some remarks on the dominating sets of the annihilating-ideal graph of a commutative ring
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 383-412

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The rings considered in this article are commutative with identity which admit at least one nonzero annihilating ideal. Let R be a ring. Let 𝔸(R) denote the set of all annihilating ideals of R and let us denote 𝔸(R)\{(0)} by 𝔸(R)^∗. Recall that the annihilating-ideal graph of R, denoted by 𝔸𝔾(R) is an undirected graph whose vertex set is 𝔸(R)^∗ and distinct vertices I and J are adjacent if and only if IJ = (0). The aim of this article is to generalize some of the known results on the domination number of 𝔸𝔾(R). We also determine the domination number of two spanning supergraphs of 𝔸𝔾(R) in the case of a reduced ring R.
Keywords: annihilating-ideal graph, minimal prime ideal, maximal N-prime of $(0)$, reduced ring, domination number of a graph 
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Visweswaran, Subramanian. Some remarks on the dominating sets of the annihilating-ideal graph of a commutative ring. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 383-412. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a9/