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Non-comaximal graph of ideals of a ring

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Abstract

Let R be a ring. The non-comaximal graph of R, denoted by NC(R) is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of R and any two distinct vertices I and J are adjacent if and only if \(I+J\ne R\). The concepts of connectedness, independent set, clique and traversability of NC(R) are discussed.

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Acknowledgements

This paper is the outcome of INSPIRE Summer Research Project 2017, Department of Science and Technology, Government of India of the first author (INSPIRE Registration No. 201300036277, Application Reference No. DST/INSPIRE/02/2013/026713).

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Authors and Affiliations

  1. Department of Mathematics, Cotton University, Guwahati, 781 001, India

    Bikash Barman & Kukil Kalpa Rajkhowa

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  1. Bikash Barman
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  2. Kukil Kalpa Rajkhowa
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Correspondence to Kukil Kalpa Rajkhowa.

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Communicating Editor: Sharad S Sane

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Barman, B., Rajkhowa, K.K. Non-comaximal graph of ideals of a ring. Proc Math Sci 129, 76 (2019). https://doi.org/10.1007/s12044-019-0504-x

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  • DOI: https://doi.org/10.1007/s12044-019-0504-x

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