环的强零因子图的一个注记 |
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引用本文: | 赵贤,;唐高华. 环的强零因子图的一个注记[J]. 广西师范学院学报(自然科学版), 2008, 0(4): 15-17 |
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作者姓名: | 赵贤, 唐高华 |
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作者单位: | [1]梧州学院数理系,广西梧州543002; [2]广西师范学院数学与计算机科学系,广西南宁530001 |
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基金项目: | Supported by National Natural Science Foundation of China (10771095), Guangxi Natural Science Foundation ( 0575052, 0832107 ), Innovation Project of Guangxi Graduate Education (2007106030701M15) and Scientific Research Foundation of Guangxi Educational Committee |
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摘 要: | 一个环R的一个元α叫做一个强零因子,假如对R中的某个非零元b,有〈α〉〈b〉=0,或者〈b〉〈α〉=0(其中〈x〉是由x∈R生成的理想).在该文中,用S(R)表示所有强零因子的集合.对于任意的一个环r,用^~Г(R)表示一个无向图,它的顶点集是S(R)^*=S(R)-{0},其中两上不同的顶点α和b相连当且仅当〈n〉〈b〉=0或者〈b〉〈α〉=0.该文主要研究质环直积的强零因子图的团数.
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关 键 词: | 强零因子 强零因子图 团数 |
A Note on Strong Zero-divisor Graphs of Rings |
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Affiliation: | ZHAO Xian, TANG Gao-hua (1. Department of Mathematics and Physics, Wuzhou University, Wuzhou 543002, P. R. China; 2. Department of Mathematics and Computer Science, Guangxi Teachers Education University, Nanning 530001, P. R. China) |
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Abstract: | An dement a in a ring R is caled a strong zero-divisor if either 〈 α 〉 〈 b 〉 = 0 or 〈 b 〉 〈 α 〉 = 0, for someO≠b∈R(〈x〉 is the ideal generated by x∈R). Let S(R) denote the set of strong zero-divisors of R. The strong zero-divisor graph .~Г (R) is an undirected graph with vertices S (R)^* ( = S (R) - { 0 } ), where distinct vertices a and b are adjacent if and only if either 〈 α 〉 〈 b 〉 = 0 or 〈 b 〉 〈 α 〉 = 0. In this note, we study the number of cliques of the strong zero-divlsor graph of a direct product of prime rings. |
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Keywords: | strong zero-divisor strong zero-divisor clique |
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