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Cut vertices in comaximal graph of a commutative Artinian ring

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Abstract

Let R be a commutative Artinian ring with \(|{\text{Max}}(R)|=n \ge 2\). We show the comaximal graph of R has no cut-sets with more than one vertex. It has exactly a cut vertex if and only if \(R \simeq F\times \mathbb {Z}_2 \times \cdots \times \mathbb {Z}_2\), where F is a field, \(\vert F \vert > 2\) and \(n \ge 3\). It has n cut vertices if and only if R is a Boolean ring.

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Correspondence to Karim Samei.

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Communicated by Sharad S Sane.

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Esmaili, K., Samei, K. Cut vertices in comaximal graph of a commutative Artinian ring. Indian J Pure Appl Math 52, 340–343 (2021). https://doi.org/10.1007/s13226-021-00119-3

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  • DOI: https://doi.org/10.1007/s13226-021-00119-3

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