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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| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
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irk-123456789-1547722019-06-16T01:31:09Z Modules whose maximal submodules have τ-supplements Buyukasık, E. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/154772 en Algebra and Discrete Mathematics 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 |
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. |
| format |
Article |
| author |
Buyukasık, E. |
| spellingShingle |
Buyukasık, E. Modules whose maximal submodules have τ-supplements Algebra and Discrete Mathematics |
| author_facet |
Buyukasık, E. |
| author_sort |
Buyukasık, E. |
| title |
Modules whose maximal submodules have τ-supplements |
| title_short |
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_sort |
modules whose maximal submodules have τ-supplements |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154772 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT buyukasıke moduleswhosemaximalsubmoduleshavetsupplements |
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2023-05-20T17:45:21Z |
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2023-05-20T17:45:21Z |
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