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On the genus of reduced cozero-divisor graph of commutative rings

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Abstract

Let R be a commutative ring with identity and let (x) be the principal ideal generated by \(x\in R.\) Let \(\varOmega (R)^*\) be the set of all nontrivial principal ideals of R. The reduced cozero-divisor graph \(\varGamma _r(R)\) of R is an undirected simple graph with \(\varOmega (R)^*\) as the vertex set and two distinct vertices (x) and (y) in \(\varOmega (R)^*\) are adjacent if and only if \((x)\nsubseteq (y)\) and \((y)\nsubseteq (x)\). In this paper, we characterize all classes of commutative Artinian non-local rings for which the reduced cozero-divisor graph has genus at most one.

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Funding

This research work is supported by CSIR Emeritus Scientist Scheme (No. 21 (1123)/20/EMR-II) of Council of Scientific and Industrial Research, Government of India through the third author.

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  1. Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, 627012, Tamil Nadu, India

    E. Jesili, K. Selvakumar & T. Tamizh Chelvam

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  1. E. Jesili
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  2. K. Selvakumar
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  3. T. Tamizh Chelvam
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Correspondence to T. Tamizh Chelvam.

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This research work is supported by CSIR Emeritus Scientist Scheme (No. 21 (1123)/20/EMR-II) of Council of Scientific and Industrial Research, Government of India through the third author.

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Jesili, E., Selvakumar, K. & Tamizh Chelvam, T. On the genus of reduced cozero-divisor graph of commutative rings. Soft Comput 27, 657–666 (2023). https://doi.org/10.1007/s00500-022-07616-5

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