H -supplemented modules with respect to a preradical
Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and on...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2011 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154821 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727291571798016 |
|---|---|
| author | Talebi, Y. Moniri Hamzekolaei, A. R. Tutuncu, D. K. |
| author_facet | Talebi, Y. Moniri Hamzekolaei, A. R. Tutuncu, D. K. |
| citation_txt | H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and only if M₁ and M₂ are τ-H-supplemented. Secondly, let M=⊕ⁿi=1Mi be a τ-supplemented module. Assume that Mi is τ-Mj-projective for all j>i. If each Mi is τ-H-supplemented, then M is τ-H-supplemented. We also investigate the relations between τ-H-supplemented modules and τ-(⊕-)supplemented modules.
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| first_indexed | 2025-12-07T19:02:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154821 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:02:08Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Talebi, Y. Moniri Hamzekolaei, A. R. Tutuncu, D. K. 2019-06-16T05:31:52Z 2019-06-16T05:31:52Z 2011 H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16S90, 16D10, 16D70, 16D99. https://nasplib.isofts.kiev.ua/handle/123456789/154821 Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and only if M₁ and M₂ are τ-H-supplemented. Secondly, let M=⊕ⁿi=1Mi be a τ-supplemented module. Assume that Mi is τ-Mj-projective for all j>i. If each Mi is τ-H-supplemented, then M is τ-H-supplemented. We also investigate the relations between τ-H-supplemented modules and τ-(⊕-)supplemented modules. The authors would like to thank Prof. R. Wisbauer and the referee for their helpfulcomments and carefully reading this article en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics H -supplemented modules with respect to a preradical Article published earlier |
| spellingShingle | H -supplemented modules with respect to a preradical Talebi, Y. Moniri Hamzekolaei, A. R. Tutuncu, D. K. |
| title | H -supplemented modules with respect to a preradical |
| title_full | H -supplemented modules with respect to a preradical |
| title_fullStr | H -supplemented modules with respect to a preradical |
| title_full_unstemmed | H -supplemented modules with respect to a preradical |
| title_short | H -supplemented modules with respect to a preradical |
| title_sort | h -supplemented modules with respect to a preradical |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154821 |
| work_keys_str_mv | AT talebiy hsupplementedmoduleswithrespecttoapreradical AT monirihamzekolaeiar hsupplementedmoduleswithrespecttoapreradical AT tutuncudk hsupplementedmoduleswithrespecttoapreradical |