Prime intersection graph of ideals of a ring

被引：4

作者：

Rajkhowa, Kukil Kalpa ^{[1
]}

Saikia, Helen K. ^{[2
]}

机构：

[1] Cotton Univ, Dept Math, Gauhati 781001, India

[2] Gauhati Univ, Dept Math, Gauhati 781014, India

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2020年 / 130卷 / 01期

关键词：

Prime intersection graph; ring; prime ideal; connected graph;

D O I：

10.1007/s12044-019-0541-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 boolean AND J not equal 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).

引用

页数：12

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