Classical Artinian Module and Related Topics

Abed, Majid Mohammed; Al-Sharqi, Faisal

doi:10.1088/1742-6596/1003/1/012065

Cited by 16 publications

(6 citation statements)

References 2 publications

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“…63, No. 6, pp: 2650-26552651 Many algebraic structures were studied such as rings, ideals, submodules, and modules [1][2][3][4][5][6]. Some researchers have studied neutrosophic of some algebraic concepts such as neutrosophic set, neutrosophic submodule, neutrosophic module, neutrosophic group, and neutrosophic ring in general [7,8,9,10,11].…”

Section: Abedmentioning

confidence: 99%

On Indeterminacy (Neutrosophic ) of Hollow Modules

Abed

2022

eijs

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In this paper, we formulate and study a new property, namely indeterminacy (neutrosophic) of the hollow module. We mean indeterminacy hollow module is neutrosophic hollow module B (shortly Ne(B)) such that it is not possible to specify the conditions for satisfying it. Some concepts have been studied and introduced, for instance, the indeterminacy local module, indeterminacy divisible module, indeterminacy indecomposable module and indeterminacy hollow-lifting module. Also, we investigate that if Ne(B) is an indeterminacy divisible module with no indeterminacy zero divisors, then any indeterminacy submodule Ne(K) of Ne(B) is an indeterminacy hollow module. Further, we study the relationship between the indeterminacy of hollow and indecomposable modules. Finally, conclusions and discussions for our obtained results are given.

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Section: Abedmentioning

confidence: 99%

On Indeterminacy (Neutrosophic ) of Hollow Modules

Abed

2022

eijs

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“…In [10], any module B over integral domain is said to be divisible if tB=B, t ∈ T. So 𝐵 1 ≤ 𝐵 any submodule B1 of B is called almost max-submodule if and only if 𝐵 1 is large maximal submodule (shortly La-max-submodule) if and only if B1 is a maximal submodule. More details about algebraic structures which related to this article in ( [11], [12], [13]). Semi 𝑻-Small Submodules in [14].…”

Section: Introductionmentioning

confidence: 99%

Generalization of Local Modules

Abed

2024

Iraqi Journal of Science

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In this paper we introduce a generalization of local module. The notion of 2-Local module can be considered a new concept (generalization of local modules). Let T be a ring with identity. 2-maximal submodule can define as, any submodule B1 of B is called 2-maximal if (B/B1) is a 2-regular module. 2-Local module means every submodule A of a T-module B where is a unique 2-maximal submodule. Almost any unique maximal submodule of a T-module gives 2-local module. Also, we can present a generalization of local module by, if is a fully prime module over the ring and every submodule B1 of a T-module B is a unique almost max-submodule, this means is a 2-local. Every semi-maximal submodule over chained module is maximal (2-maximal submodule) and hence is 2-local module. Some properties and examples of 2-Local module are given. Finally some implications of 3-local module have been presented.

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“…Some results of neutrosophic topological rings [10]. More details about the relations and some applications in [11][12][13][14] This paper is about to introduced neutrosophic of relations in group theory like homomorphism and equivalent relations such as reflexive, symmetric and transitive.…”

Section: Introductionmentioning

confidence: 99%

On Neutrosophic Relations in Group Theory

Abed

Jarwan

Salih

2023

ijmscs

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In this paper, we study neutrosophic of some triple relations or neutrosophic triple set (NTS) and related to the homomorphism groups. Various properties like equivalent relation, product, intersection and the union are studied. We showed several equivalent relations in group theory with new examples about neutrosophic homomorphism. Finally, some definitions, examples and other remarks of neutrosophic of these relations are given.

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Classical Artinian Module and Related Topics

Cited by 16 publications

References 2 publications

On Indeterminacy (Neutrosophic ) of Hollow Modules

On Indeterminacy (Neutrosophic ) of Hollow Modules

Generalization of Local Modules

On Neutrosophic Relations in Group Theory

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