PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE

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Bijari Homa; Kashyarmanesh Kazem; Fazaeli Moghimi Hosein

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2020 | Volume:8 | Issue:1 Page(s): 53-68

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Information Journal Paper

Title

PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE

Author(s)

Bijari Homa | Kashyarmanesh Kazem | Fazaeli Moghimi Hosein | Issue Writer Certificate

Keywords

Primary spectrum

primary Zariski topology

primary submodule

prime ideal

Abstract

Let R be a commutative ring with identity and let M be an R-module. We define the Primary spectrum of M, denoted by PS(M), to be the set of all primary submodules Q of M such that (radQ: M)=(Q: M)− − − − − − √ . In this paper, we topologize PS(M) with a topology having the Zariski topology on the prime spectrum Spec(M) as a subspace topology. We investigate compactness and irreducibility of this topological space and provide some conditions under which PS(M) is a spectral space.

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APA: Copy

Bijari, Homa, Kashyarmanesh, Kazem, & Fazaeli Moghimi, Hosein. (2020). PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE. JOURNAL OF ALGEBRAIC SYSTEMS, 8(1 ), 53-68. SID. https://sid.ir/paper/382420/en

Vancouver: Copy

Bijari Homa, Kashyarmanesh Kazem, Fazaeli Moghimi Hosein. PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2020;8(1 ):53-68. Available from: https://sid.ir/paper/382420/en

IEEE: Copy

Homa Bijari, Kazem Kashyarmanesh, and Hosein Fazaeli Moghimi, “PRIMARY ZARISKI TOPOLOGY ON THE PRIMARY SPECTRUM OF A MODULE,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 8, no. 1 , pp. 53–68, 2020, [Online]. Available: https://sid.ir/paper/382420/en

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