Zero Divisor Graph of a Poset with Respect to an Ideal

被引：38
|
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
收藏
页码：499 / 506
页数：8
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