H -supplemented modules with respect to a preradical
Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and on...
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| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154821 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-1548212019-06-17T01:31:04Z H -supplemented modules with respect to a preradical Yahya Talebi A. R. Moniri Hamzekolaei Derya Keskin Tutuncu Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and only if M₁ and M₂ are τ-H-supplemented. Secondly, let M=⊕ⁿi=1Mi be a τ-supplemented module. Assume that Mi is τ-Mj-projective for all j>i. If each Mi is τ-H-supplemented, then M is τ-H-supplemented. We also investigate the relations between τ-H-supplemented modules and τ-(⊕-)supplemented modules. 2011 Article H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16S90, 16D10, 16D70, 16D99. http://dspace.nbuv.gov.ua/handle/123456789/154821 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 a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and only if M₁ and M₂ are τ-H-supplemented. Secondly, let M=⊕ⁿi=1Mi be a τ-supplemented module. Assume that Mi is τ-Mj-projective for all j>i. If each Mi is τ-H-supplemented, then M is τ-H-supplemented. We also investigate the relations between τ-H-supplemented modules and τ-(⊕-)supplemented modules. |
| format |
Article |
| author |
Yahya Talebi A. R. Moniri Hamzekolaei Derya Keskin Tutuncu |
| spellingShingle |
Yahya Talebi A. R. Moniri Hamzekolaei Derya Keskin Tutuncu H -supplemented modules with respect to a preradical Algebra and Discrete Mathematics |
| author_facet |
Yahya Talebi A. R. Moniri Hamzekolaei Derya Keskin Tutuncu |
| author_sort |
Yahya Talebi |
| title |
H -supplemented modules with respect to a preradical |
| title_short |
H -supplemented modules with respect to a preradical |
| title_full |
H -supplemented modules with respect to a preradical |
| title_fullStr |
H -supplemented modules with respect to a preradical |
| title_full_unstemmed |
H -supplemented modules with respect to a preradical |
| title_sort |
h -supplemented modules with respect to a preradical |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154821 |
| citation_txt |
H -supplemented modules with respect to a preradical/ Yahya Talebi, A. R. Moniri Hamzekolaei, Derya Keskin Tutuncu // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 116–131. — Бібліогр.: 16 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:45:22Z |
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