The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-09-21 DOI:10.4995/agt.2022.16332

Saif Salam, K. Al-Zoubi

引用次数: 1

Abstract

Let R be a G-graded ring and M be a G-graded R-module. We define the graded primary spectrum of M, denoted by PSG(M), to be the set of all graded primary submodules Q of M such that (GrM(Q) :RM) = Gr((Q:RM)). In this paper, we define a topology on PSG(M) having the Zariski topology on the graded prime spectrum SpecG(M) as a subspace topology, and investigate several topological properties of this topological space.

查看原文本刊更多论文

渐变交换环上渐变模的渐变初级谱上的Zariski拓扑

设R为g级环，M为g级R模。我们定义M的分级主谱，用PSG(M)表示为M的所有分级主子模Q的集合，使得(GrM(Q):RM) = Gr((Q:RM))。本文定义了PSG(M)上具有分级素谱SpecG(M)上Zariski拓扑的拓扑作为子空间拓扑，并研究了该拓扑空间的若干拓扑性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.