The Annihilating-Ideal Graph of an Idealization

被引：0
|
作者：
Ahrari, M. [1 ]
Sabet, Sh. A. Safari [1 ]
Amini, B. [2 ]
机构：
[1] Islamic Azad Univ, Cent Tehran Branch, Dept Math, Tehran, Iran
[2] Shiraz Univ, Dept Math, Coll Sci, Shiraz, Iran
来源：
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE | 2017年 / 41卷 / A1期
关键词：
Annihilating-ideal graph; Idealization; Girth; Diameter;
D O I：
10.1007/s40995-017-0185-1
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The annihilating-ideal graph of a commutative ring R is denoted by AG(R), whose vertices are all nonzero ideals of R with nonzero annihilators and two distinct vertices I and J are adjacent if and only if IJ - 0. In this paper, we consider the annihilating-ideal graphs of idealizations of commutative rings. We study the behavior of the girth and diameter of the annihilating-ideal graph of a commutative ring when extending to idealizations of the ring.
引用
收藏
页码：165 / 168
页数：4
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