论文标题
分级模块具有noetherian分级的第二光谱
Graded modules with Noetherian graded second spectrum
论文作者
论文摘要
让$ r $为$ g $分级的交换戒指，$ m $是$ g $ raded $ r $ $摩德。 $ m $的所有分级第二个划线的集合用$ spec_g^s（m）$表示，并且称为$ m $的分级第二频谱。在本文中，我们讨论了Noetherian评分的原始频谱的评分环，并得出一些结论。此外，我们介绍了分级分节模型的分级Zariski Socle的概念，并探索其特性。使用这些结论和属性，我们还从Zariski拓扑的角度研究了$ spec_g^s（m）$，从成为noetherian空间并提供一些相关结果的角度。
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 $Spec_G^s(M)$ and it is called the graded second spectrum of $M$. In this paper, we discuss graded rings with Noetherian graded prime spectrum and obtain some conclusions. In addition, we introduce the notion of the graded Zariski socle of graded submodules and explore their properties. Using these conclusions and properties, we also investigate $Spec_G^s(M)$ with the Zariski topology from the viewpoint of being a Noetherian space and give some related outcomes.
