All finitely generated<i>M</i>-subgenerated modules are extending

Vanaja, N.

doi:10.1080/00927879608825585

Cited by 20 publications

(6 citation statements)

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“…The different generalizations of this theorem can be found in [13][14][15]. In the present paper we study the rings satisfying conditions which are more general than conditions 2) and 3) of Theorem.…”

Section: )mentioning

confidence: 99%

I*0-Modules

Abyzov

2014

Russ Math.

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Section: )mentioning

confidence: 99%

I*0-Modules

Abyzov

2014

Russ Math.

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“…= 0 with i j in I, it follows from proposition 2.2 of (Vanaja, 1996) that N = ⊕ i∈I N i and N i ∈ σ[M i ]. As, for each i ∈ I, N i is Dedekind finite then, N i is finitely generated.…”

Section: Propositionmentioning

confidence: 99%

On FGDF-modules

Ba¹,

Toure²,

Diankha³

2017

JMR

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Let R be a unital ring and M a unitary module not necessary over R. The FGDF-module is a generalization of FGDFrings (Touré, Diop, Mohamed and Sangharé, 2014). In this work, we first give some properties of FGDF-modules. After that, we show that for a finitely generated module M, M is a FGDF-module if and only if M is of finite representation type module. Finally, we show that M is a finitely generated FGDF-module if and only if every Dedekind finite module of σ[M] is noetherian.

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“…The study of rings over which finitely generated right modules are CS was initiated by Dung and Smith [4]. It was shown further in Huynh, Rizvi and Yousif [9] and Vanaja [12] that such rings must be right Noetherian. Huynh and Rizvi [10] recently investigated rings over which every countably generated right module is a direct sum of a projective module and a CS-module, and they showed that these rings form a special class of right Artinian rings.…”

Section: Introductionmentioning

confidence: 99%

Decompositions of modules into projective modules and CS-modules

Plubtieng¹

2000

Bull. Austral. Math. Soc.

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Let M be a right R-module. It is shown that M is a locally Noetherian module if every finitely generated module in σ[M] is a direct sum of a projective module and a CS-module. Moreover, if every module in σ[M] is a direct sum of a projective module and a CS-module, then every module in σ[M] is a direct sum of modules which are either indecomposable projective or uniform Σ-quasi-injective. In particular, if every module in σ[M] is a direct sum of a projective module and a quasi-continuous module, then every module in σ[M] is a direct sum of a projective module and a quasi-injective module.

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All finitely generatedM-subgenerated modules are extending

Cited by 20 publications

References 4 publications

I*0-Modules

I*0-Modules

On FGDF-modules

Decompositions of modules into projective modules and CS-modules

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