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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154772 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Modules whose maximal submodules have τ-supplements |
| spellingShingle |
Modules whose maximal submodules have τ-supplements Buyukasık, E. |
| 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 |
| author |
Buyukasık, E. |
| author_facet |
Buyukasık, E. |
| publishDate |
2010 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
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Інститут прикладної математики і механіки НАН України |
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Article |
| 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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| url |
https://nasplib.isofts.kiev.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. |
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2025-12-07T16:28:25Z |
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2025-12-07T16:28:25Z |
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1850867612711387136 |