Some remarks on Φ-sharp modules
The purpose of this paper is to introduce some new classes of modules which is closely related to the classes of sharp modules, pseudo-Dedekind modules and TV-modules. In this paper we introduce the concepts of Φ-sharp modules, Φ-pseudo-Dedekind modules and Φ-TV-modules. Let R be a commutative ring...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156638 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Some remarks on Φ-sharp modules / A.Y. Darani, M. Rahmatinia // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 209-220. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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nasplib_isofts_kiev_ua-123456789-1566382025-02-09T12:28:51Z Some remarks on Φ-sharp modules Darani, A.Y. Rahmatinia, M. The purpose of this paper is to introduce some new classes of modules which is closely related to the classes of sharp modules, pseudo-Dedekind modules and TV-modules. In this paper we introduce the concepts of Φ-sharp modules, Φ-pseudo-Dedekind modules and Φ-TV-modules. Let R be a commutative ring with identity and set H={M∣M is an R-module and Nil(M) is a divided prime submodule of M}. For an R-module M∈H, set T=(R∖Z(M))∩(R∖Z(R)), T(M)=T−1(M) and P:=(Nil(M):RM). In this case the mapping Φ:T(M)⟶MP given by Φ(x/s)=x/s is an R-module homomorphism. The restriction of Φ to M is also an R-module homomorphism from M in to MP given by Φ(m/1)=m/1 for every m∈M. An R-module M∈H is called a Φ-sharp module if for every nonnil submodules N,L of M and every nonnil ideal I of R with N⊇IL, there exist a nonnil ideal I′⊇I of R and a submodule L′⊇L of M such that N=I′L′. We prove that Many of the properties and characterizations of sharp modules may be extended to Φ-sharp modules, but some can not. 2017 Article Some remarks on Φ-sharp modules / A.Y. Darani, M. Rahmatinia // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 209-220. — Бібліогр.: 22 назв. — англ. 1726-3255 2010 MSC:Primary 16N99, 16S99; Secondary 06C05, 16N20. https://nasplib.isofts.kiev.ua/handle/123456789/156638 en Algebra and Discrete Mathematics application/pdf Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The purpose of this paper is to introduce some new classes of modules which is closely related to the classes of sharp modules, pseudo-Dedekind modules and TV-modules. In this paper we introduce the concepts of Φ-sharp modules, Φ-pseudo-Dedekind modules and Φ-TV-modules. Let R be a commutative ring with identity and set H={M∣M is an R-module and Nil(M) is a divided prime submodule of M}. For an R-module M∈H, set T=(R∖Z(M))∩(R∖Z(R)), T(M)=T−1(M) and P:=(Nil(M):RM). In this case the mapping Φ:T(M)⟶MP given by Φ(x/s)=x/s is an R-module homomorphism. The restriction of Φ to M is also an R-module homomorphism from M in to MP given by Φ(m/1)=m/1 for every m∈M. An R-module M∈H is called a Φ-sharp module if for every nonnil submodules N,L of M and every nonnil ideal I of R with N⊇IL, there exist a nonnil ideal I′⊇I of R and a submodule L′⊇L of M such that N=I′L′. We prove that Many of the properties and characterizations of sharp modules may be extended to Φ-sharp modules, but some can not. |
| format |
Article |
| author |
Darani, A.Y. Rahmatinia, M. |
| spellingShingle |
Darani, A.Y. Rahmatinia, M. Some remarks on Φ-sharp modules Algebra and Discrete Mathematics |
| author_facet |
Darani, A.Y. Rahmatinia, M. |
| author_sort |
Darani, A.Y. |
| title |
Some remarks on Φ-sharp modules |
| title_short |
Some remarks on Φ-sharp modules |
| title_full |
Some remarks on Φ-sharp modules |
| title_fullStr |
Some remarks on Φ-sharp modules |
| title_full_unstemmed |
Some remarks on Φ-sharp modules |
| title_sort |
some remarks on φ-sharp modules |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156638 |
| citation_txt |
Some remarks on Φ-sharp modules / A.Y. Darani, M. Rahmatinia // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 209-220. — Бібліогр.: 22 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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2025-11-25T23:55:28Z |
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2025-11-25T23:55:28Z |
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