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

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 ${\mathcal{P}\mathcal{S}}_G(M)$, to be the set of all graded primary submodules $Q$ of M such that $(G{r}_M(Q){:}_{R}M)=Gr((Q{:}_{R}M))$. In this paper, we define a topology on ${\mathcal{P}\mathcal{S}}_G(M)$ having the Zariski topology on the graded prime spectrum $Spe{c}_G(M)$ as a subspace topology, and investigate several topological properties of this topological space.

Cited by in corpus (1)

• Graded modules with Noetherian graded second spectrum