Modules that have a supplement in every cofinite extension

Çalışıcı, Hamza; Türkmen, Ergül

doi:10.1515/gmj-2012-0018

Cited by 9 publications

(13 citation statements)

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“…al., 2017) respectively and some basic properties of them are investigated. While preparing this paper besides the article (Özdemir, 2016), the articles (Çalışıcı et al, 2012 andTürkmen, 2013) related with modules having a supplement and Rad-supplement in every cofinite extension are used. Generalized   supplementing modules are of course a generalization of injective modules such as Zöschinger's modules with the property () E .…”

Section:  mentioning

confidence: 99%

“…al., 2017) respectively and some basic properties of them are investigated. While preparing this paper besides the article (Özdemir, 2016), the articles (Çalışıcı et al, 2012 andTürkmen, 2013) related with modules having a supplement and Rad-supplement in every cofinite extension are used. Throughout the paper, By (Zhou, 2000), a submodule (Koşan, 2007) and (Wang, 2007).…”

Section: Structured Abstractmentioning

confidence: 99%

“…al., 2006). In a recent paper, (Çalışıcı and Türkmen, 2012), modules that have a supplement in every cofinite extension have been studied and these modules are called modules with the property (CE)((CEE)). After this paper, generalization of these modules has been studied in (Türkmen, 2013).…”

Section: Turkish Studies -Information Technologies and Applied Sciencmentioning

confidence: 99%

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Rad-Tümleyenli̇ Modülleri̇n Yeni̇ Bi̇r Genelleşti̇ri̇lmesi̇

Eryilmaz¹,

Sözen²

2019

TurkishStudies

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Section:  mentioning

confidence: 99%

“…al., 2017) respectively and some basic properties of them are investigated. While preparing this paper besides the article (Özdemir, 2016), the articles (Çalışıcı et al, 2012 andTürkmen, 2013) related with modules having a supplement and Rad-supplement in every cofinite extension are used. Throughout the paper, By (Zhou, 2000), a submodule (Koşan, 2007) and (Wang, 2007).…”

Section: Structured Abstractmentioning

confidence: 99%

Section: Turkish Studies -Information Technologies and Applied Sciencmentioning

confidence: 99%

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Rad-Tümleyenli̇ Modülleri̇n Yeni̇ Bi̇r Genelleşti̇ri̇lmesi̇

Eryilmaz¹,

Sözen²

2019

TurkishStudies

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“…Then, N is called an extension of M by K. To simplify the notation, we think of M as a submodule N . In [3], a module N is said to be a cofinite extension of M provided M Â N and N M is finitely generated. In light of this fact that finitely generated modules are coatomic, we call a module N coatomic extension of M if the factor module N M of N is coatomic.…”

Section: Introductionmentioning

confidence: 99%

“…In [3], a module M is said to have the property .CE/ (respectively, the property .CEE/) if M has a supplement (respectively, ample supplements) in every cofinite extension. It is shown in [3,Theorem 2.12] that R is semiperfect if and only if every left R-module has the property .CE/.…”

Section: Introductionmentioning

confidence: 99%

Modules that have a supplement in every coatomic extension

Türkmen¹

2015

MMN

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Let R be a ring and M be an R-module. M is said to be an E-module (respectively, an EE-module) if M has a supplement (respectively, ample supplements) in every coatomic extension N , i.e. N M is coatomic. We prove that if a module M is an EE-module, every submodule of M is an E-module, and then we show that a ring R is left perfect iff every left R-module is an E-module iff every left R-module is an EE-module. We also prove that the class of E-modules is closed under extension. In addition, we give a new characterization of left V-rings by cofinitely injective modules.

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Modules that have a weak supplement in every extension

Önal¹,

Çalışıcı²,

Türkmen³

2016

MMN

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We say that over an arbitrary ring a module M has the property .WE/ (respectively, .WEE/) if M has a weak supplement (respectively, ample weak supplements) in every extension. In this paper, we provide various properties of modules with these properties. We show that a module M has the property .WEE/ iff every submodule of M has the property .WE/. A ring R is left perfect iff every left R-module has the property .WE/ iff every left R-module has the property .WEE/. A ring R is semilocal iff every left R-module has a weak supplement in every extension with small radical. We also study modules that have a weak supplement(respectively, ample weak supplements) in every coatomic extension, namely the property .WE /(respectively, .WEE /).

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Modules that have a supplement in every cofinite extension

Cited by 9 publications

References 0 publications

Rad-Tümleyenli̇ Modülleri̇n Yeni̇ Bi̇r Genelleşti̇ri̇lmesi̇

Rad-Tümleyenli̇ Modülleri̇n Yeni̇ Bi̇r Genelleşti̇ri̇lmesi̇

Modules that have a supplement in every coatomic extension

Modules that have a weak supplement in every extension

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