伽罗瓦环的高斯扩张的零因子图的性质  

The Properties of Zero-divisor Graph for Gauss Extension of A Galois Ring

作　　者：陈蔚凝 唐高华 CHEN Wei-ning;TANG Gao-hua(School of Mathematics and Statistics,Nanning Normal University,Nanning 530299,China;School of Sciences,Beibu Gulf University,Qinzhou 535011,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530299 [2]北部湾大学理学院,广西钦州535011

出　　处：《南宁师范大学学报（自然科学版）》2020年第2期7-11,共5页Journal of Nanning Normal University：Natural Science Edition

基　　金：This work was supported by the National Natural Science Foundation of China(11661013,11661014,11961050);the Scientific Research Foundation of Guangxi Educational Committee(KY2016YB276).

摘　　要：设R是一个交换环,R的零因子图,记为Γ(R),是以R的非零零因子集合作为顶点集,两个不同的顶点x与y相连当且仅当xy=0.该文完全刻画了伽罗瓦环的高斯扩张的零因子图的直径与围长,同时给出了伽罗瓦环的高斯扩张的零因子图成为平面图的一个充分必要条件.Let R be a commutative ring.The zero divisor graph of R,denoted byΓ(R),is a graph whose vertex set is the set of all non-zero zero-divisors of R,and two distinct vertices xand yare adjacent if and only if xy=0.In this paper,we completely characterize the diameter and girth of the zero-divisor graph of the Gauss extension of a Galois ring.We also present a necessary and sufficient condition for the zero-divisor graph of the Gauss extension of a Galois ring being planar.

关 键 词：伽罗瓦环 高斯扩张 零因子图 

分 类 号：O15[理学—数学]