Modules whose maximal submodules have τ-supplements
Let R be a ring and τ be a preradical for the category of left R-modules. In this paper, we study on modules whose maximal submodules have τ-supplements. We give some characterizations of these modules in terms their certain submodules, so called τ-local submodules. For some certain preradicals τ,...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154772 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modules whose maximal submodules have τ-supplements / E. Buyukasık // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 1–9. — Бібліогр.: 8 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862696817045536768 |
|---|---|
| author | Buyukasık, E. |
| author_facet | Buyukasık, E. |
| citation_txt | Modules whose maximal submodules have τ-supplements / E. Buyukasık // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 1–9. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let R be a ring and τ be a preradical for the category of left R-modules. In this paper, we study on modules whose maximal submodules have τ-supplements. We give some characterizations of these modules in terms their certain submodules, so called τ-local submodules. For some certain preradicals τ, i.e. τ=δ and idempotent τ, we prove that every maximal submodule of M has a τ-supplement if and only if every cofinite submodule of M has a τ-supplement. For a radical τ on R-Mod, we prove that, for every R-module every submodule is a τ-supplement if and only if R/τ(R) is semisimple and τ is hereditary.
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| first_indexed | 2025-12-07T16:28:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154772 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| language | English |
| last_indexed | 2025-12-07T16:28:25Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Buyukasık, E. 2019-06-15T20:44:20Z 2019-06-15T20:44:20Z 2010 Modules whose maximal submodules have τ-supplements / E. Buyukasık // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 1–9. — Бібліогр.: 8 назв. — англ. 2000 Mathematics Subject Classification:16D10, 16N80 https://nasplib.isofts.kiev.ua/handle/123456789/154772 Let R be a ring and τ be a preradical for the category of left R-modules. In this paper, we study on modules whose maximal submodules have τ-supplements. We give some characterizations of these modules in terms their certain submodules, so called τ-local submodules. For some certain preradicals τ, i.e. τ=δ and idempotent τ, we prove that every maximal submodule of M has a τ-supplement if and only if every cofinite submodule of M has a τ-supplement. For a radical τ on R-Mod, we prove that, for every R-module every submodule is a τ-supplement if and only if R/τ(R) is semisimple and τ is hereditary. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Modules whose maximal submodules have τ-supplements Article published earlier |
| spellingShingle | Modules whose maximal submodules have τ-supplements Buyukasık, E. |
| title | Modules whose maximal submodules have τ-supplements |
| title_full | Modules whose maximal submodules have τ-supplements |
| title_fullStr | Modules whose maximal submodules have τ-supplements |
| title_full_unstemmed | Modules whose maximal submodules have τ-supplements |
| title_short | Modules whose maximal submodules have τ-supplements |
| title_sort | modules whose maximal submodules have τ-supplements |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154772 |
| work_keys_str_mv | AT buyukasıke moduleswhosemaximalsubmoduleshaveτsupplements |