Classification of Rings with Toroidal and Projective Coannihilator Graph

Abdulaziz M. Alanazi, Mohd Nazim, Nadeem Ur Rehman and Marco Fontana

Journal of Mathematics, 2021, vol. 2021, 1-7

Abstract: Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS or β∉αβS, where δS denotes the principal ideal generated by δ∈S. In this study, we first classify finite ring S, for which AG′S is isomorphic to some well-known graph. Then, we characterized the finite ring S, for which AG′S is toroidal or projective.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4384683

DOI: 10.1155/2021/4384683

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