理想化的互极大图 |
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引用本文: | 吴国磊,;徐卉,;居腾霞. 理想化的互极大图[J]. 南通工学院学报(自然科学版), 2014, 0(2): 71-75 |
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作者姓名: | 吴国磊, 徐卉, 居腾霞 |
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作者单位: | [1]南通大学理学院,江苏南通226007; [2]如皋高等师范学校数理与信息技术系,江苏南通226500 |
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基金项目: | 基金项目:国家自然科学基金项目(11271208) |
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摘 要: | 设R是有1的交换环, M是R-模, R(+)M是环R对于R-模M的理想化。讨论了理想化R(+)M的理想、极大理想和可逆元与环R的理想、极大理想和可逆元之间的联系,并利用理想化的代数性质,讨论了R(+)M的互极大图的子图Γ2(R(+)M)-J(R(+)M)的直径和围长。
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关 键 词: | 互极大图 Jacobson根 理想化 交换环 可逆元 |
Comaximal Graph of Idealizations |
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Affiliation: | WU Guolei, XU Hui, JU Tengxia (1. School of Sciences, Nantong University, Nantong 226007, China; 2. Department of Mathematics Physics and Information Technology, Rugao Normal College, Nantong 226500, China) |
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Abstract: | Let R be a commutative ring with an identity 1, M be an R-module, and R(+)M be the idealization of the ring R by the R-module M, the relationship between ideals, maximal ideals and unit elements of idealization R(+)M and those of ring R were discussed. The algebraic properties was also used to study the diameter and girth of the sub-graphΓ2 (R(+)M)-J(R(+)M) of comaximal graph of the idealization R(+)M. |
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Keywords: | comaximal graph Jacobson radical idealization commutative ring invertible element |
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