Some remarks on Φ-sharp modules
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Some remarks on Φ-sharp modules
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| Creator |
Darani, A.Y.
Rahmatinia, M. |
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| 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.
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| Date |
2019-06-18T18:18:27Z
2019-06-18T18:18:27Z 2017 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/156638 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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