A new topology over the primary-like spectrum of a module

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-10-01 DOI:10.4995/agt.2021.13225

F. Rashedi

引用次数: 0

Abstract

Let R be a commutative ring with identity and M a unitary R-module. The primary-like spectrum SpecL(M) is the collection of all primary-like submodules Q of M, the recent generalization of primary ideals, such that M/Q is a primeful R-module. In this article, we topologies SpecL(M) with the patch-like topology, and show that when, SpecL(M) with the patch-like topology is a quasi-compact, Hausdorff, totally disconnected space.

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模块的类主谱上的新拓扑

设R是一个恒等交换环，M是一个酉R模。类初等谱SpecL(M)是M的所有类初等子模Q的集合，是初等理想的最新推广，使得M/Q是一个素数r模。在本文中，我们对具有类patch拓扑的SpecL(M)进行拓扑化，并证明当，具有类patch拓扑的SpecL(M)是一个准紧的、Hausdorff的、完全不连通的空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.