Graded modules with Noetherian graded second spectrum

被引：1
|
作者：
Salam, Saif [1 ]
Al-Zoubi, Khaldoun [1 ]
机构：
[1] Jordan Univ Sci & Technol, Dept Math & Stat, POB 3030, Irbid 22110, Jordan
来源：
AIMS MATHEMATICS | 2023年 / 8卷 / 03期
关键词：
graded second submodule; graded second spectrum; graded Zariski socle; Zariski topology; Noetherian graded second spectrum; PRIME;
D O I：
10.3934/math.2023335
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let R be a G graded commutative ring and M be a G-graded R-module. The set of all graded second submodules of M is denoted by S pec(G)(s)(M), and it is called the graded second spectrum of M. We discuss graded rings with Noetherian graded prime spectrum. In addition, we introduce the notion of the graded Zariski socle of graded submodules and explore their properties. We also investigate S pec(G)(s)(M) with the Zariski topology from the viewpoint of being a Noetherian space.
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页码：6626 / 6641
页数：16
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