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Blow up; projective bundle; nef cone; chow 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 $I \cap J \neq 0$ 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 $G_{P}(\mathbb{Z}_{n})$. The core part of this paper is observed in the ring $\mathbb{Z}_{n}$.

KUKIL KALPA RAJKHOWA¹ HELEN K SAIKIA²

1. Department of Mathematics, Cotton University, Guwahati 781 001, India
2. Department of Mathematics, Gauhati University, Guwahati 781 014, India

Published

30 January 2020

Manuscript received

8 November 2018

Manuscript revised

29 March 2019

Accepted

26 July 2019

Early published

Unedited version published online

Final version published online

25 January 2020