群环Z_n[i]G的零因子图的性质
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摘要
本文主要研究由模n高斯整数环Z_n[i]和素数阶循环群G构成的群环Z_n[i]G的零因子图的性质,分别给出了Z_n[i]G的零因子图的围长、平面性和直径的完全刻画。
Let Gbe a cyclic group with prime order,Z_n[i]be the Guassian integers modulo nand Z_n[i]G be the group ring of Gover Z_n[i].Properties of the zero-divisor graph of Z_n[i]Gare investigated in this paper and the girth,the planarity and the diameter of the zero-divisor graph of Z_n[i]G are completely characterized respectively.
Let Gbe a cyclic group with prime order,Z_n[i]be the Guassian integers modulo nand Z_n[i]G be the group ring of Gover Z_n[i].Properties of the zero-divisor graph of Z_n[i]Gare investigated in this paper and the girth,the planarity and the diameter of the zero-divisor graph of Z_n[i]G are completely characterized respectively.
引文
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[2]ANDERSON D F,LIVINGSTON P S.The zero-divisor graph of a commutative ring[J].Journal of Algebra,1999,217(2):434-447.DOI:10.1006/jabr.1998.7840.
[3]唐高华,苏华东,易忠.Zn[i]的单位群结构[J].广西师范大学学报(自然科学版),2010,28(2):38-41.DOI:10.16088/j.issn.1001-6600.2010.02.004.
[4]苏华东,唐高华.Zn[i]的素谱和零因子[J].广西师范学院学报(自然科学版),2006,23(4):1-4.DOI:10.16601/j.cnki.issn1001-8743.2006.04.001.
[5]唐高华,苏华东,赵寿祥.Zn[i]的零因子图的性质[J].广西师范大学学报(自然科学版),2007,25(3):32-35.DOI:10.16088/j.issn.1001-6600.2007.03.002.
[6]SU Huangdong.Central sets and radii of the zero-divisor graph of Gaussian integers modulo n[J].Guangxi Sciences,2012,19(3):221-223.DOI:10.13656/j.cnki.gxkx.2012.03.019.
[7]郭述锋,谢光明,易忠.群环ZnG的零因子图的性质[J].广西师范大学学报(自然科学版),2015,33(2):68-75.DOI:10.16088/j.issn.1001-6600.2015.02.011.
[8]BONDY J A,MURT U S R.图论及其应用[M].吴望名,译.北京:科学出版社,1984:163.
[9]LAM T Y.A first course in noncommutative rings[M].New York:Spring-Verlag,1991:299.
[10]潘承洞,潘承彪.初等数论[M].北京:北京大学出版社,1992:231.
[11]MILIES C P,SEHGAL S K.An introduction to group rings[M].Dordrecht:Kluwer Academic Publishers,2002:154.
[12]OSBA E A,AL-ADDASI S,JARADEH N A.Zero divisor graph for the ring of Gaussian integers modulo n[J].Communications in Algebra,2008,36(10):3865-3877.
[2]ANDERSON D F,LIVINGSTON P S.The zero-divisor graph of a commutative ring[J].Journal of Algebra,1999,217(2):434-447.DOI:10.1006/jabr.1998.7840.
[3]唐高华,苏华东,易忠.Zn[i]的单位群结构[J].广西师范大学学报(自然科学版),2010,28(2):38-41.DOI:10.16088/j.issn.1001-6600.2010.02.004.
[4]苏华东,唐高华.Zn[i]的素谱和零因子[J].广西师范学院学报(自然科学版),2006,23(4):1-4.DOI:10.16601/j.cnki.issn1001-8743.2006.04.001.
[5]唐高华,苏华东,赵寿祥.Zn[i]的零因子图的性质[J].广西师范大学学报(自然科学版),2007,25(3):32-35.DOI:10.16088/j.issn.1001-6600.2007.03.002.
[6]SU Huangdong.Central sets and radii of the zero-divisor graph of Gaussian integers modulo n[J].Guangxi Sciences,2012,19(3):221-223.DOI:10.13656/j.cnki.gxkx.2012.03.019.
[7]郭述锋,谢光明,易忠.群环ZnG的零因子图的性质[J].广西师范大学学报(自然科学版),2015,33(2):68-75.DOI:10.16088/j.issn.1001-6600.2015.02.011.
[8]BONDY J A,MURT U S R.图论及其应用[M].吴望名,译.北京:科学出版社,1984:163.
[9]LAM T Y.A first course in noncommutative rings[M].New York:Spring-Verlag,1991:299.
[10]潘承洞,潘承彪.初等数论[M].北京:北京大学出版社,1992:231.
[11]MILIES C P,SEHGAL S K.An introduction to group rings[M].Dordrecht:Kluwer Academic Publishers,2002:154.
[12]OSBA E A,AL-ADDASI S,JARADEH N A.Zero divisor graph for the ring of Gaussian integers modulo n[J].Communications in Algebra,2008,36(10):3865-3877.