The Zariski Topology on the Second Spectrum of a Module

• 作者: H. Ansari-Toroghy F. Farshadifar
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: Zariski拓扑 频谱参数 子模块 谱空间 规格 交换环 集合 类似
• 年，卷（期）: 2014,（4）
• 页码范围: 671-688
• 页数: 18页
• 分类号: O153.3
• 语种: 中文

摘要

Let R be a commutative ring and M be an R-module. The second spectrum Spec^S(M) of M is the collection of all second submodules of M. We topologize Spec^S(M) with Zariski topology, which is analogous to that for Spec(R), and investigate this topolog- ical space. For various types of modules M, we obtain conditions under which Spec^S(M) is a spectral space. We also investigate Specs (M) with quasi-Zariski topology.