| 环的直积的零因子图 |
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| 引用本文： | 刘琼,陈莉.环的直积的零因子图[J].上海电力学院学报,2014,30(2):185-187. |
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| 作者姓名： | 刘琼 陈莉 |
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| 作者单位： | [1]上海电力学院数理学院,上海200090 [2]盐城师范学院数学科学学院,江苏盐城224002 |
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| 基金项目： | 国家自然科学基金（11201407）. |
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| 摘 要： | 研究了交换环的直积R1×R2的零因子图.对于交换环R1和R2,讨论了零因子图Γ(R1×R2)的直径与围长,分别确定了当图Γ(R1×R2)的直径为1,2,3时,对应的交换环R1和R2的代数结构,并给出了环的等价表述.
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| 关 键 词： | 交换环 整环 零因子图 直积 代数结构 |
| 收稿时间： | 3/3/2014 12:00:00 AM |
Zero-divisor Graph of the Direct Product of Commutative Rings |
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| LIU Qiong and CHEN Li.Zero-divisor Graph of the Direct Product of Commutative Rings[J].Journal of Shanghai University of Electric Power,2014,30(2):185-187. |
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| Authors: | LIU Qiong and CHEN Li |
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| Affiliation: | 1. School of Mathematics and Physics Science, Shanghai University of Electric Power, Shanghai 200090, China ; 2. School of Mathematics Science, Yancheng Teachers University, Yancheng 224002, China) |
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| Abstract: | The zero-divisor graphs of the direct product of commutative rings is studied. For any commutative ring R1 and R2, attention is focused on the diameter of R1×R2, and the algebraic structure of R1 ,RE, is determined where the diameter of F（R1×R2 ） is 1,2, or 3. Furthermore, the equivalent characterization of the diameter of the zero-divisor graph of R1×R2 is presented. |
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| Keywords: | commutative rings domain zero-divisor graph direct product algebraic structure |
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