Cut vertices in comaximal graph of a commutative Artinian ring

Kyuoomars Esmaili () and Karim Samei ()
Additional contact information
Kyuoomars Esmaili: Malayer University
Karim Samei: Malayer University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 340-343

Abstract: Abstract Let R be a commutative Artinian ring with $$|{\text{Max}}(R)|=n \ge 2$$ | Max ( R ) | = n ≥ 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 $$R \simeq F\times \mathbb {Z}_2 \times \cdots \times \mathbb {Z}_2$$ R ≃ F × Z 2 × ⋯ × Z 2 , where F is a field, $$\vert F \vert > 2$$ | F | > 2 and $$n \ge 3$$ n ≥ 3 . It has n cut vertices if and only if R is a Boolean ring.

Keywords: Comaximal graph; Cut vertex; Cut-set; 13A99 (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-021-00119-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00119-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-021-00119-3

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().