Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules

In this paper, we define and study the notion of intuitionistic fuzzy classical primary submodules over a unitary $R$-module $M$, where $R$ is a commutative ring with unity. This is a generalisation of intuitionistic fuzzy primary ideals and intuitionistic fuzzy classical prime submodules. We further topologize the collection of all intuitionistic fuzzy submodules on an $R$-module $M$ with a topology having the intuitionistic fuzzy primary Zariski topology on the intuitionistic fuzzy classical primary spectrum $IF_{cp}spec(M)$ as a subspace topology and investigate the properties of this topological space.

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Publication Details

Journal
Notes on Intuitionistic Fuzzy Sets
Published
2024-10-01
DOI
https://doi.org/10.7546/nifs.2024.30.3.203-214
Primary Topic
Fuzzy and Soft Set Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules

P. K. Sharma
Notes on Intuitionistic Fuzzy Sets
Fuzzy and Soft Set Theory
article

Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules

P. K. Sharma
article en

Abstract

In this paper, we define and study the notion of intuitionistic fuzzy classical primary submodules over a unitary $R$-module $M$, where $R$ is a commutative ring with unity. This is a generalisation of intuitionistic fuzzy primary ideals and intuitionistic fuzzy classical prime submodules. We further topologize the collection of all intuitionistic fuzzy submodules on an $R$-module $M$ with a topology having the intuitionistic fuzzy primary Zariski topology on the intuitionistic fuzzy classical primary spectrum $IF_{cp}spec(M)$ as a subspace topology and investigate the properties of this topological space.

Notes on Intuitionistic Fuzzy SetsVol. 30(3)
Openalex Percentile: Top 79%
Fuzzy and Soft Set Theory
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Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules — P. K. Sharma · Notes on Intuitionistic Fuzzy Sets (2024) | TGRS Research Map | TGRS