交换环的二部本质图  

Bipartite Essential Graphs of Commutative Rings

作　　者：谷伟平[1] 张倩玉 赵英英 GU Weiping;ZHANG Qianyu;ZHAO Yingying(School of Electromechanical and Information Engineering,Chongqing College of Humanities Science and Technology,Chongqing 401524,China;Department of Construction and Economic Management,Shandong Urban Construction Vocational College,Jinan 250103,China)

机构地区：[1]重庆人文科技学院机电与信息工程学院,重庆401524 [2]山东城市建设职业学院建筑经济管理系,山东济南250103

出　　处：《信阳师范学院学报（自然科学版）》2020年第1期37-41,共5页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11501467);重庆人文科技学院科研项目(CRK2020001-ZK)

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.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.

关 键 词：交换环 零因子图 本质图 二部图 

分 类 号：O151.21[理学—数学]