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- W4313646093 abstract "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." @default.
- W4313646093 created "2023-01-07" @default.
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- W4313646093 date "2023-01-01" @default.
- W4313646093 modified "2023-10-18" @default.
- W4313646093 title "Graded modules with Noetherian graded second spectrum" @default.
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- W4313646093 doi "https://doi.org/10.3934/math.2023335" @default.
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