Journal of Guangxi Normal University(Natural Science Edition) ›› 2016, Vol. 34 ›› Issue (1): 66-71.doi: 10.16088/j.issn.1001-6600.2016.01.010

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

GUO Shufeng1,2 , XIE Guangming2, YI Zhong2,3   

  1. 1.School of Mathematical Sciences,Capital Normal University,Beijing 100048,China;
    2.College of Mathematics and Statistics ,Guangxi Normal University,Guilin Guangxi 541004,China;
    3. Guilin University of Aerospace Technology ,Guilin Guangxi 541004,China
  • Received:2015-07-27 Published:2018-09-14

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Abstract: 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 G be a cyclic group of prime order, ZnG group rings of G over Zn and Δ(G)augmentation ideals of ZnG. Properties of zero-divisor graphs of idealizations of ZnG with respect to Δ(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 ZnG,respectively.

Key words: group ring, zero-divisor graph, girth, diameter, planarity

CLC Number: 

  • O153.3
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