| 交换环的二部本质图 |
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| 作者单位： | ;1.重庆人文科技学院机电与信息工程学院;2.山东城市建设职业学院建筑经济管理系 |
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| 摘 要： | 交换环R的本质图EG(R)是一个无向简单图,它以Z(R){0}为顶点集,两个不同的顶点x、y之间有一条边相连当且仅当ann(xy)是R的一个本质理想.给出了模n剩余类环Zn的零因子图与本质图相等的充分必要条件.在此基础上,证明了交换环的二部本质图必是完全二部图,并对相应的环进行了同构分类.
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| 关 键 词： | 交换环 零因子图 本质图 二部图 |
Bipartite Essential Graphs of Commutative Rings |
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| Affiliation: | ,School of Electromechanical and Information Engineering,Chongqing College of Humanities Science and Technology,Department of Construction and Economic Management,Shandong Urban Construction Vocational College |
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| Abstract: | For a commutative ringR, its essential graphEG(R) is an undirected simple graph whose vertex set is Z(R) {0}, and two distinct verticesxandyare adjacent if and only if ann(xy) is an essential ideal. By giving a necessary and sufficient condition forZnsuch that its zero-divisor graph coincides with its essential graph, it is showed that a bipartite essential graph of a commutative ring must be a complete bipartite graph, and the classifications of the corresponding rings up to isomorphism are also established. |
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| Keywords: | commutative ring zero-divisor graph essential graph bipartite graph |
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