Large-Maximal submodules

Abduljaleel, Amira A.; Yaseen, Sahira M.

doi:10.1088/1742-6596/1963/1/012011

Cited by 3 publications

(2 citation statements)

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“…But La-max-submodule is maximal in case 𝐵 is semisimple module. Now from [20], we study some properties of hollow and local modules. Also other modules have some relations with 2-local modules which is namely chained and semi-simple modules.…”

Section: Proofmentioning

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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Section: Proofmentioning

confidence: 99%

Generalization of Local Modules

Abed

2024

Iraqi Journal of Science

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“…A proper submodule of an R-module is named maximal in [3] "if whenever is a submodule of R-Module with Implies . Abduljaleel and Yaseen in [2] offer the concept of large maximal submodules as a generalization of the concept maximal submodules, "where a proper submodule of an Rmodule is named large-maximal(L-maximal) if implies is an essential submodule of , where a submodule of R-module is named essential, if for every non-zero submodule of , [3]. Many authors studies module and submodule for example see [4] and [5].…”

Section: Introductionmentioning

confidence: 99%

Pure Maximal Submodules and Related Concepts

Ahmed,

Al. Mothafar

2023

IHJPAS

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In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule of an R-module is called Pr- maximal if ,for any submodule of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule of an R-module is named near (N-maximal) whensoever is pure submodule of such that then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of is Pr-maximal. A ring is named Pr-ring if whole proper ideal of is a Pr-maximal ideal, we offer the concept pure local (Pr-local) module an R-module is named pure local (Pr-local) module. If it has only a Pr-maximal submodule which includes all proper submodule of . A ring is named pure local (Pr-local) ring, if is a Pr-local R-module. We give some relatio among Pr-maximal submodules and others related concept.

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Some submodules related to (P.V.M)

Saleh,

Abed

2023

PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonline

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Large-Maximal submodules

Cited by 3 publications

References 2 publications

Generalization of Local Modules

Generalization of Local Modules

Pure Maximal Submodules and Related Concepts

Some submodules related to (P.V.M)

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