群环Z_nG的理想化零因子图的性质  

Properties of Zero-divisor Graphs of Idealizations of Group Rings Z_nG

作　　者：郭述锋[1,2] 谢光明[2] 易忠[2,3] 

机构地区：[1]首都师范大学数学科学学院,北京100048 [2]广西师范大学数学与统计学院,广西桂林541004 [3]桂林航天工业学院,广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2016年第1期66-71,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11161005);北京市教育委员会科技计划重点项目(KZ201410028033)

摘　　要：研究环的零因子图,以图的方式清晰、直观地刻画环的零因子的结构,这对理解环的结构本身具有重要意义。本文主要讨论了群环Z_nG关于增广理想Δ(G)的理想化Z_nG(+)Δ(G)的零因子图的性质,分别给出了环Z_nG(+)Δ(G)的零因子图的围长、直径和平面性的详细刻画,其中G为素数阶群。It is very important to understand the structure of the ring itself by studying the zero-divisor graph of a ring to clearly and intuitively describe the structure of its zero-divisors by means of graph.Let Gbe a cyclic group of prime order,Z_n G group rings of Gover Z_n and Δ（G）augmentation ideals of Z_nG.Properties of zero-divisor graphs of idealizations of Z_n G with respect toΔ（G）are discussed in this paper.It provides detailed descriptions of the girth,the diameter and the planarity of zero-divisor graphs of idealizations of Z_n G,respectively.

关 键 词：群环 零因子图 围长 直径 平面性 

分 类 号：O153.3[理学—数学]