On the prime spectrum of modules

Ansari-Toroghy, H.; Pourmortazavi, Seyed Sajad

doi:10.18514/mmn.2015.1102

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2022

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Cited by 2 publications

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“…In recent years, the study of modules whose spectra space have a Zariski topology has grown in various directions. Some researchers have investigated the interplay between algebraic properties of a module and the topological properties of its spectrum (see for example [1,2,6,7,8,15,17,23,24,26,30,32]). Also the Zariski topology on the graded spectrum of graded rings in [33,34,35,36,37] was generalized in different ways to the graded spectrum of graded modules over graded commutative rings as in [3,4,13,14,33].…”

Section: Introductionmentioning

confidence: 99%

The Graded Classical Prime Spectrum with the Zariski Topology as a Notherian Topological Space

Jaradat¹

2022

IJMSI

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Section: Introductionmentioning

confidence: 99%

The Graded Classical Prime Spectrum with the Zariski Topology as a Notherian Topological Space

Jaradat¹

2022

IJMSI

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Zariski topology on the spectrum of fuzzy classical primary submodules

Panpho

Yiarayong

2022

Appl. Gen. Topol.

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Let R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.

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On the prime spectrum of modules

Abstract: Abstract. Let R be a commutative ring and let M be an R-module. Let us denote the set of all prime submodules of M by Spec.M /. In this article, we explore more properties of strongly top modules and investigate some conditions under which Spec.M / is a spectral space.

Cited by 2 publications

References 11 publications

The Graded Classical Prime Spectrum with the Zariski Topology as a Notherian Topological Space

The Graded Classical Prime Spectrum with the Zariski Topology as a Notherian Topological Space

Zariski topology on the spectrum of fuzzy classical primary submodules

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