The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring
Submitted: 2021-09-20
|Accepted: 2022-05-29
|Published: 2022-10-03
Copyright (c) 2022 Applied General Topology
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Keywords:
graded primary submodules, graded primary spectrum, Zariski topology
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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.
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