Fuzzy submodules: some analogues and deviations

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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“…and the inverse image of 𝔹 denoted by 𝑓 −1 (𝔹) ∈ 𝐹𝑆𝐸(𝕄)𝑖𝑠 defined by: ᵮ −1 (𝔹)(𝑥) = 𝔹(ᵮ(𝑥)), for all ∈ 𝕄 [15][16] .…”

Section: Definitionmentioning

confidence: 99%

“…Let 𝕏 ∈FUM(𝕄 1 ) and 𝕐 ∈FM(𝕄 2 ). ℊ ∶ 𝕏 → 𝕐 is called a fuzzy homomorphism if ℊ: 𝕄 1 → 𝕄 2 is 𝔽-homomorphism and 𝕐(ℊ(𝒽) = 𝕏(𝒽) for each 𝒽 ∈ 𝕄 1 [15] .…”

Section: Definitionmentioning

confidence: 99%

Fully Fuzzy Visible Modules With Other Related Concepts

Mohammed

Shihab

2023

IHJPAS

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“…In 1987, Pan [23] introduced the construction of fuzzy finitely generated modules. The product of a fuzzy ideal and a fuzzy submodule and the sum of two fuzzy submodules were defined by Kumar et al [19] in 1995. Several researchers have studied the concept of fuzzy submodules in different fields.…”

Section: Introductionmentioning

confidence: 99%

A new type of the hybrid algebra between Abelian groups and UP (BCC)-algebras: UP (BCC)-modules

Polhinkong,

Ngenkokkruad,

Chinram

et al. 2023

J. Math. Computer Sci.

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The goal of this study is to introduce the concept of a new type of the hybrid algebra between Abelian groups and UP (BCC)-algebras: UP (BCC)-modules. We introduce the concept of fuzzy UP (BCC)-submodules of UP (BCC)-modules and provide properties and find the necessary and sufficient conditions for this concept. We define fuzzy sets in UP (BCC)-modules of many forms, supplying their properties and their relation to fuzzy UP (BCC)-submodules. We also define and study the fuzzy UP (BCC)-submodule generated by a set of fuzzy sets in UP (BCC)-modules, as well as provide for their properties and their relation to fuzzy UP (BCC)-submodules. Finally, we apply the concept of fuzzy UP (BCC)-ideals of UP (BCC)-algebras while providing properties and find the results of the composition and the product between fuzzy UP (BCC)-ideals and fuzzy UP (BCC)-submodules.

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“…The concepts of fuzzy modules and fuzzy submodules were first introduced by Negoita and Ralescu in 1975 [3]. Consequently, fuzzy finitely generated submodules, fuzzy quotient modules [4], radical of fuzzy submodules and primary fuzzy submodules [5,6] were investigated and Saikia and Kalita [7] established fuzzy essential submodules and looked into their different properties.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Soc-T-ABSO Sub-Modules

Marie

Khalaf

2022

ijcsm

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This research analyses the correlation that exists between fuzzy T-ABSO and fuzzy socle. To answer this question, we define a new concept called, fuzzy socle T-ABSO submodules. Results showed many properties that satisfied the new notion. In addition, we applied some algebra operations and found the relationship between fuzzy T-ABSO and fuzzy socle -T-ABSO. We also investigated the structure of fuzzy socle T-ABSO sub- modules of a module under fuzzy direct sum, homomorphic image and intersection. Moreover, the relation between fuzzy socle T-ABSO sub-module and other types of fuzzy sub-module was presented. The implications of this study could be used to define new concepts that depend on fuzzy socle T-ABSO concepts

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Fuzzy submodules: some analogues and deviations

Cited by 10 publications

References 7 publications

Fully Fuzzy Visible Modules With Other Related Concepts

Fully Fuzzy Visible Modules With Other Related Concepts

A new type of the hybrid algebra between Abelian groups and UP (BCC)-algebras: UP (BCC)-modules

Fuzzy Soc-T-ABSO Sub-Modules

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