Rad-⊕-Supplemented Modules and Cofinitely Rad-⊕-Supplemented Modules

Ecevit, Şule; Koşan, M. Tamer; Tribak, Rachid

doi:10.1142/s1005386712000508

Cited by 13 publications

(9 citation statements)

References 7 publications

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“…It is clear that every ⊕-supplemented module is Rad-⊕-supplemented. For the concept of Rad-⊕-supplemented, we refer to [14] and [13].…”

Section: And Corollary 26])mentioning

confidence: 99%

On a variation of ⊕-supplemented modules

Kaynar

2023

Preprint

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Let R be a ring and M be an R-module. M is called ⊕ss-supplemented if every submodule of M has a ss-supplement that is a direct summand of M. In this paper, the basic properties and characterizations of ⊕ss-supplemented modules are provided. In particular, it is shown that (1) if a module M is ⊕ss-supplemented, then Rad(M) is semisimple and Soc(M) ⊴ M, (2) every direct sum of ss-lifting modules is ⊕ss-supplemented; (3) a commutative ring R is an artinian serial ring with semisimple radical if and only if every left R-module is ⊕ss-supplemented. MSC Classification: 16D10 , 16D60 , 16D99

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“…It is clear that every ⊕-supplemented module is Rad-⊕-supplemented. For the concept of Rad-⊕-supplemented, we refer to [14] and [13].…”

Section: And Corollary 26])mentioning

confidence: 99%

On a variation of ⊕-supplemented modules

Kaynar

2023

Preprint

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“…The submodules Rad(M ) and δ(M ) have very important roles in modules theory, so that related to these submodules, many generalizations of small and δ−small modules are introduced and investigated by some authors. We refer for some of them to [2,4,5,7,8,10].…”

Section: If Every Proper Submodule Ofmentioning

confidence: 99%

Torsion Theory and its Applications in M − D Modules

Talaee

2014

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“…More details about generalized (radical) supplemented modules are in [13]. More details about generalized (radical) ⊕−supplemented modules are in [1,3]. More informations about g-supplemented modules are in [5].…”

Section: Introductionmentioning

confidence: 99%

Strongly ⊕−g−radical supplemented modules

Özdemir¹,

Nebiyev²

2023

MMN

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In this work, strongly ⊕ − g−radical supplemented modules are defined and some properties of these modules are investigated. Every ring has unity and every module is unital left module in this work. It is proved that every direct summand of a strongly ⊕ − g−radical supplemented module is strongly ⊕ − g−radical supplemented. Let f : M −→ N be an R−module epimorphism and Ker ( f ) be a direct summand of M. If M is strongly ⊕ − g−radical supplemented, then N is also strongly ⊕ − g−radical supplemented. Let M be a strongly ⊕ − g− radical supplemented R−module and K ≤ M. If V is a g-radical supplement submodule in M for every g-radical supplement submodule V /K in M/K, then M/K is strongly ⊕ − g−radical supplemented.

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Rad-⊕-Supplemented Modules and Cofinitely Rad-⊕-Supplemented Modules

Cited by 13 publications

References 7 publications

On a variation of ⊕-supplemented modules

On a variation of ⊕-supplemented modules

Torsion Theory and its Applications in M − D Modules

Strongly ⊕−g−radical supplemented modules

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