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Classification of Rings with Toroidal and Projective Coannihilator Graph

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  • Abdulaziz M. Alanazi
  • Mohd Nazim
  • Nadeem Ur Rehman
  • Marco Fontana

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.

Suggested Citation

  • Abdulaziz M. Alanazi & Mohd Nazim & Nadeem Ur Rehman & Marco Fontana, 2021. "Classification of Rings with Toroidal and Projective Coannihilator Graph," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, June.
    • Handle: RePEc:hin:jjmath:4384683
    DOI: 10.1155/2021/4384683
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