Prime intersection graph of ideals of a ring

Let R be a ring. The prime intersection graph of ideals of R , denoted by G P ( R ) , is the graph whose vertex set is the collection of all non-trivial (left) ideals of R with two distinct vertices I and J are adjacent if and only if I ∩ J ≠ 0 and either one of I or J is a prime ideal of R . We dis...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2020-12, Vol.130 (1), Article 17
Main Authors: Rajkhowa, Kukil Kalpa, Saikia, Helen K
Format: Article
Language:English
Subjects:
Apexes
Mathematics
Mathematics and Statistics
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Summary:Let R be a ring. The prime intersection graph of ideals of R , denoted by G P ( R ) , is the graph whose vertex set is the collection of all non-trivial (left) ideals of R with two distinct vertices I and J are adjacent if and only if I ∩ J ≠ 0 and either one of I or J is a prime ideal of R . We discuss connectedness in G P ( R ) . The concepts of bipartition, planarity and colorability are interpreted. Finally, we introduce the idea of traversability in G P ( Z n ) . The core part of this paper is observed in the ring Z n .
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-019-0541-5