Journal of Guangxi Normal University(Natural Science Edition) ›› 2010, Vol. 28 ›› Issue (2): 38-41.

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Structure of the Unit Group of Zn[i]

TANG Gao-hua1, SU Hua-dong1, YI Zhong2   

  1. 1. School of Mathematics Science,Guangxi Teachers Education University,Nanning Guangxi 530001,China;
    2. College of Mathematical Science,Guangxi Normal University,Guilin Guangxi541004,China
  • Received:2009-12-05 Online:2010-06-20 Published:2023-02-07

Abstract: In 1801,Gauss proved the structure theorem of the unit group U(Zn) of the residue class ring Zn and constructed Gaussianintegers ring Z[i]=｛a+bi｜a,b∈Z,i2=-1｝ over complex plane and the problem of two-square-sum in number theory was solved.The structure of the unit group of the Gaussian integers ring module n:Zn[i]=｛a+bi｜a,b∈Zn｝ is not solved until today.In this paper,by combining methodsinnumber theory,combinatorics and algebra,the structure of the unit group U(Zn[i]) are completely determined.

Key words: Guassian integers modulo n, unit group, cyclic group

CLC Number: 

  • O153.3
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