| 交换环上的形式矩阵环的零因子和零因子图（英文） |
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| 引用本文： | 唐高华,李玉,苏华东.交换环上的形式矩阵环的零因子和零因子图（英文）[J].数学进展,2019(1):99-109. |
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| 作者姓名： | 唐高华 李玉 苏华东 |
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| 作者单位： | 北部湾大学理学院;南宁师范大学数学与统计科学学院;西南大学数学与统计学院 |
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| 基金项目： | supported by NSFC(Nos.11661014,11461010,11661013);the Guangxi Science Research and Technology Development Project(No.1599005-2-13);the Guangxi Natural Science Foundation(Nos.2016GXSFDA380017,2016GXNSFCA380014);the Scientific Research Fund of Guangxi Education Department(No.KY2015ZD075) |
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| 摘 要： | 本文主要研究交换环R上的形式矩阵环M_n(R;{Sijk})的零因子和零因子图.首先给出了环上形式线性方程组的概念,并且得到了交换环上形式齐次线性方程组有非平凡解的充分必要条件.然后证明了A是M_n(R;{Sijk})的零因子当且仅当A的行列式是R的零因子当且仅当A是RA]的零因子.最后研究了交换环R上的形式矩阵环M_n(R;{Sijk})的零因子图的性质.
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| 关 键 词： | 形式矩阵环 形式线性方程组 零因子 零因子图 |
Zero-divisors and Zero-divisor Graphs of Formal Matrix Rings over a Commutative Ring |
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| TANG Gaohua,LI Yu,SU Huadong.Zero-divisors and Zero-divisor Graphs of Formal Matrix Rings over a Commutative Ring[J].Advances in Mathematics,2019(1):99-109. |
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| Authors: | TANG Gaohua LI Yu SU Huadong |
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| Institution: | (School of Sciences,Beibu Gulf University,Qinzhou,Guangxi,535011,P.R.China;School of Mathematics and Statistics,Nanning Normal University,Nanning,Guangxi,530023,P.R.China;School of Mathematics and Statistics,Southwest University,Chongqing,400715,P.R.China) |
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| Abstract: | TANG Gaohua;LI Yu;SU Huadong(School of Sciences,Beibu Gulf University,Qinzhou,Guangxi,535011,P.R.China;School of Mathematics and Statistics,Nanning Normal University,Nanning,Guangxi,530023,P.R.China;School of Mathematics and Statistics,Southwest University,Chongqing,400715,P.R.China) |
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| Keywords: | formal matrix ring system of formal linear equations zero-divisor zero-divisor graph |
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