Zero Divisor Graph of a Poset with Respect to an Ideal

被引：39

作者：

Joshi, Vinayak ^{[1
]}

机构：

[1] Univ Pune, Dept Math, Pune 411007, Maharashtra, India

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2012年 / 29卷 / 03期

关键词：

Zero divisor graph; Clique number; Chromatic number; Annihilator; Semi-ideal; Ideal; Prime ideal; Semiprime ideal; COMMUTATIVE RING;

D O I：

10.1007/s11083-011-9216-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce the zero divisor graph G (I) (P) of a poset P (with 0) with respect to an ideal I. It is shown that G (I) (P) is connected with its diameter <= 3, and if G (I) (P) contains a cycle, then the core K of G (I) (P) is a union of 3-cycles and 4-cycles. Further, the chromatic number and clique number of G (I) (P) are shown to be equal. This proves a form of Beck's conjecture for posets with 0. The complete bipartite zero divisor graphs are characterized.

引用

页码：499 / 506

页数：8

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