Distributive Modules

Erdoğdu, V.

doi:10.4153/cmb-1987-035-x

Cited by 27 publications

(8 citation statements)

References 2 publications

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“…Recall that an R-module M is called distributive module if for all submodules A,B and C of M , A ( ) ( ) ( ) for more details see [6].…”

Section: Proposition (25)mentioning

confidence: 99%

On Strong Dual Rickart Modules

Kamil

2022

eijs

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Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to define strong dual Rickart module. Let M and N be R- modules , M is called N- strong dual Rickart module (or relatively sd-Rickart to N)which is denoted by M it is N-sd- Rickart if for every submodule A of M and every homomorphism fHom (M , N) , f (A) is a direct summand of N. We prove that for an R- module M , if R is M-sd- Rickart , then every cyclic submodule of M is a direct summand . In particular, if M is projective, then M is Z-regular. We give various characterizations and basic properties of this type of modules.

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“…Recall that an R-module M is called distributive module if for all submodules A,B and C of M , A ( ) ( ) ( ) for more details see [6].…”

Section: Proposition (25)mentioning

confidence: 99%

On Strong Dual Rickart Modules

Kamil

2022

eijs

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“…Recall that an R-module M is called distributive if A  (B + C) =(A  B)+(A  C) for all submodules A, B and C of M, [11]. Now, we give another condition under which, the direct sum of max-CS is max-CS.…”

Section: Ismentioning

confidence: 99%

On The Direct Sum Of Min(Max) - CS Modules

Hadi¹,

Majeed²

2013

Jour. Kufa Math. Comp.

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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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Distributive Modules

Abstract: Let R be a commutative ring with identity. An R-module M is said to be distributive if the lattice of submodules of M is distributive. We characterize such modules and study their properties.

Cited by 27 publications

References 2 publications

On Strong Dual Rickart Modules

On Strong Dual Rickart Modules

On The Direct Sum Of Min(Max) - CS Modules

On distributive semimodules

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