A study on dual square free modules
Let M be an H-supplemented coatomic module with FIEP. Then we prove that M is dual square free if and only if every maximal submodule ofM is fully invariant. Let M = ⊕ i∈I Mi be a direct sum, such that M is coatomic. Then we prove that M is dual square free if and only if each Mi is dual square free...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188753 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A study on dual square free modules / M. Medina-Bárcenas, D. Keskin Tütüncü, Y. Kuratomi // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 267-279. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Let M be an H-supplemented coatomic module with FIEP. Then we prove that M is dual square free if and only if every maximal submodule ofM is fully invariant. Let M = ⊕ i∈I Mi be a direct sum, such that M is coatomic. Then we prove that M is dual square free if and only if each Mi is dual square free for all i ∈ I and, Mi and ⊕ j̸≠i Mj are dual orthogonal. Finally we study the endomorphism rings of dual square free modules. Let M be a quasi-projective module. If EndR(M) is right dual square free, then M is dual square free. In addition, if M is finitely generated, then EndR(M) is right dual square free whenever M is dual square free. We give several examples illustrating our hypotheses.
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| ISSN: | 1726-3255 |