Preradicals and characteristic submodules: connections and operations
For an arbitrary module M∈R-Mod the relation between the lattice Lch(RM) of characteristic (fully invariant) submodules of M and big lattice R-pr of preradicals of R-Mod is studied. Some isomorphic images of Lch(RM) in R-pr are constructed. Using the product and coproduct in R-pr four operations...
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| Дата: | 2010 |
|---|---|
| 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/123456789/154603 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Preradicals and characteristic submodules: connections and operations / A.I. Kashu // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 59–75. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-154603 |
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dspace |
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irk-123456789-1546032019-06-16T01:32:30Z Preradicals and characteristic submodules: connections and operations Kashu, A.I. For an arbitrary module M∈R-Mod the relation between the lattice Lch(RM) of characteristic (fully invariant) submodules of M and big lattice R-pr of preradicals of R-Mod is studied. Some isomorphic images of Lch(RM) in R-pr are constructed. Using the product and coproduct in R-pr four operations in the lattice Lch(RM) are defined. Some properties of these operations are shown and their relations with the lattice operations in Lch(RM) are investigated. As application the case RM=RR is mentioned, when Lch(RR) is the lattice of two-sided ideals of ring R. 2010 Article Preradicals and characteristic submodules: connections and operations / A.I. Kashu // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 59–75. — Бібліогр.: 8 назв. — англ. 1726-3255 http://dspace.nbuv.gov.ua/handle/123456789/154603 of2000 Mathematics Subject Classification:16D90, 16S90, 06B23. 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 |
For an arbitrary module M∈R-Mod the relation between the lattice Lch(RM) of characteristic (fully invariant) submodules of M and big lattice R-pr of preradicals of R-Mod is studied. Some isomorphic images of Lch(RM) in R-pr are constructed. Using the product and coproduct in R-pr four operations in the lattice Lch(RM) are defined. Some properties of these operations are shown and their relations with the lattice operations in Lch(RM) are investigated. As application the case RM=RR is mentioned, when Lch(RR) is the lattice of two-sided ideals of ring R. |
| format |
Article |
| author |
Kashu, A.I. |
| spellingShingle |
Kashu, A.I. Preradicals and characteristic submodules: connections and operations Algebra and Discrete Mathematics |
| author_facet |
Kashu, A.I. |
| author_sort |
Kashu, A.I. |
| title |
Preradicals and characteristic submodules: connections and operations |
| title_short |
Preradicals and characteristic submodules: connections and operations |
| title_full |
Preradicals and characteristic submodules: connections and operations |
| title_fullStr |
Preradicals and characteristic submodules: connections and operations |
| title_full_unstemmed |
Preradicals and characteristic submodules: connections and operations |
| title_sort |
preradicals and characteristic submodules: connections and operations |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154603 |
| citation_txt |
Preradicals and characteristic submodules: connections and operations / A.I. Kashu // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 59–75. — Бібліогр.: 8 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT kashuai preradicalsandcharacteristicsubmodulesconnectionsandoperations |
| first_indexed |
2023-05-20T17:44:58Z |
| last_indexed |
2023-05-20T17:44:58Z |
| _version_ |
1796153999658844160 |