Discussiones Mathematicae - General Algebra and Applications (Dec 2019)
On the Genus of the Co-Annihilating Graph of Commutative Rings
Abstract
Let R be a commutative ring with identity and π°R be the set of all nonzero non-units of R. The co-annihilating graph of R, denoted by ππR, is a graph with vertex set π°R and two vertices x and y are adjacent whenever ann(x) β© ann(y) = (0). In this paper, we characterize all commutative Artinian non-local rings R for which the ππR has genus one and two. Also we characterize all commutative Artinian non-local rings R for which ππR has crosscap one. Finally, we characterize all finite commutative non-local rings for which g(Π2(R)) = g(ππR) = 0 or 1.
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