Distributive modules and rings and their close analogs

Mikhalëv, A. V.; Tuganbaev, A. A.

doi:10.1007/bf02365097

Cited by 5 publications

(2 citation statements)

References 65 publications

(38 reference statements)

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“…[1], [2]. This concept for modules was studied in many papers, for example See [3], [4], [5], and [6]. In this work, we study the structure and properties of distributive semimodules.…”

Section: Introductionmentioning

confidence: 99%

On distributive semimodules

Abdulkhaliq,

Alhossaini

2023

Jour. Kufa Math. Comp.

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This work considers the construction of the concept of distributive property for semimodules. Some characterizations of this property, with some examples are given. Some conditions on semiring or semimodules (like subtractive, semisubtractive, cancellative, and k-cyclic) are required to obtain interesting results. The main results are: Any subsemimodule and factor semimodule of a distributive semimodule is distributive. Moreover, weakly distributive, is also, introduced and investigated. It is found that the semimodule is distributive if and only if each subsemimodule is weak distributive. Taking advantage of the supplemented concept to find some properties of distributive semimodule. Finally, the summand sum and summand intersection properties for distributive semimodules with some conditions are valid.

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“…[1], [2]. This concept for modules was studied in many papers, for example See [3], [4], [5], and [6]. In this work, we study the structure and properties of distributive semimodules.…”

Section: Introductionmentioning

confidence: 99%

On distributive semimodules

Abdulkhaliq,

Alhossaini

2023

Jour. Kufa Math. Comp.

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“…Distributive rings and modules are studied extensively in the literature, e.g. see [3], [7], [9], [10]. Let M be an R-module and U ⊆ M. The submodule U is said to be a distributive submodule (of M) if U = U ∩ X + U ∩ Y for all submodules X, Y ⊆ M. And M is called distributive if each submodule of M is a distributive submodule.…”

Section: Introductionmentioning

confidence: 99%

Weakly distributive modules. Applications to supplement submodules

Büyükaşık

Demirci

2010

Proc Math Sci

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Abstract. In this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive supplemented module every submodule has a unique coclosure. This generalizes a result of Ganesan and Vanaja. We prove that π -projective duo modules, in particular commutative rings, are weakly distributive. Using this result we obtain that in a commutative ring supplements are unique. This generalizes a result of Camillo and Lima. We also prove that any weakly distributive ⊕-supplemented module is quasi-discrete.

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On distributive modules and rings

Ferrero

Santana

2003

Results. Math.

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Distributive modules and rings and their close analogs

Cited by 5 publications

References 65 publications

On distributive semimodules

On distributive semimodules

Weakly distributive modules. Applications to supplement submodules

On distributive modules and rings

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