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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Бібліографічні деталі
Дата:2021
Автори: Medina-Bárcenas, M., Keskin Tütüncü, D., Kuratomi, Y.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2021
Назва видання:Algebra and Discrete Mathematics
Онлайн доступ:http://dspace.nbuv.gov.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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1887532023-03-15T01:27:28Z A study on dual square free modules Medina-Bárcenas, M. Keskin Tütüncü, D. Kuratomi, Y. 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. 2021 Article 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. 1726-3255 DOI:10.12958/adm1512 2020 MSC: 16D40, 16D70 http://dspace.nbuv.gov.ua/handle/123456789/188753 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 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.
format Article
author Medina-Bárcenas, M.
Keskin Tütüncü, D.
Kuratomi, Y.
spellingShingle Medina-Bárcenas, M.
Keskin Tütüncü, D.
Kuratomi, Y.
A study on dual square free modules
Algebra and Discrete Mathematics
author_facet Medina-Bárcenas, M.
Keskin Tütüncü, D.
Kuratomi, Y.
author_sort Medina-Bárcenas, M.
title A study on dual square free modules
title_short A study on dual square free modules
title_full A study on dual square free modules
title_fullStr A study on dual square free modules
title_full_unstemmed A study on dual square free modules
title_sort study on dual square free modules
publisher Інститут прикладної математики і механіки НАН України
publishDate 2021
url http://dspace.nbuv.gov.ua/handle/123456789/188753
citation_txt 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.
series Algebra and Discrete Mathematics
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AT keskintutuncud astudyondualsquarefreemodules
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AT medinabarcenasm studyondualsquarefreemodules
AT keskintutuncud studyondualsquarefreemodules
AT kuratomiy studyondualsquarefreemodules
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