Some Properties of the Essential Fuzzy and Closed Fuzzy Submodules

Marhon, Hassan K.; Khalaf, Hatam Y.

doi:10.24996/ijs.2020.61.4.22

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Definition Let 𝕐 ≠ ∅ and ℭ ∈ 𝐹𝑈𝑆(𝕐)1

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2024

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“…. A level set of 𝕐 with respect to ℭ denoted by the set ℭ 𝑡 , where ℭ 𝑡 ={x∈ 𝕐 ∶ ℭ (x)≥ t} ∀𝑡 ∈ [0,1], [6][7][8] .…”

Section: Definition Let 𝕐 ≠ ∅ and ℭ ∈ 𝐹𝑈𝑆(𝕐)mentioning

confidence: 99%

Fully Fuzzy Visible Modules With Other Related Concepts

Mohammed

Shihab

2023

IHJPAS

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In previous our research, the concepts of visible submodules and fully visible modules were introduced, and then these two concepts were fuzzified to fuzzy visible submodules and fully fuzzy. The main goal of this paper is to study the relationships between fully fuzzy visible modules and some types of fuzzy modules such as semiprime, prime, quasi, divisible, F-regular, quasi injective, and duo fuzzy modules, where under certain conditions it has been proven that each fully fuzzy visible module is fuzzy duo. In addition, there are many various properties and important results obtained through this research, which have been illustrated. Also, fuzzy Artinian modules and fuzzy fully stable modules have been introduced, and we study the relationships between these kinds of modules and fully fuzzy visible modules. Many other intersecting results we found.

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“…. A level set of 𝕐 with respect to ℭ denoted by the set ℭ 𝑡 , where ℭ 𝑡 ={x∈ 𝕐 ∶ ℭ (x)≥ t} ∀𝑡 ∈ [0,1], [6][7][8] .…”

Section: Definition Let 𝕐 ≠ ∅ and ℭ ∈ 𝐹𝑈𝑆(𝕐)mentioning

confidence: 99%