REDUCED ZERO-DIVISOR GRAPHS OF POSETS

被引：1

作者：

Nongsiang, Deiborlang ^{[1
]}

Saikia, Promode Kumar ^{[1
]}

机构：

[1] North Eastern Hill Univ, Dept Math, Shillong 793022, Meghalayn, India

来源：

TRANSACTIONS ON COMBINATORICS | 2018年 / 7卷 / 02期

关键词：

poset; reduced zero-divisor graph; annihilator prime ideal;

D O I：

10.22108/toc.2018.55164.1417

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates properties of the reduced zero-divisor graph of a poset. We show that a vertex is an annihilator prime ideal if and only if it is adjacent to all other annihilator prime ideals and there are always two annihilator prime ideals which are not adjacent to a non-annihilator prime ideal. We also classify all posets whose reduced zero-divisor graph is planar or toroidal and the number of distinct annihilator prime ideals is four or seven.

引用

页码：47 / 54

页数：8

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