Preradicals, closure operators in R-Mod and connection between them
For a module category R-Mod the class PR of preradicals and the class CO of closure operators are studied. The relations between these classes are realized by three mappings: Φ : CO → PR and Ψ₁, Ψ₂ : PR → CO. The impact of these mappings on the operations in PR and CO (meet, join, product, coproduct...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153348 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Preradicals, closure operators in R-Mod and connection between them / A.I. Kashu // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 86–96. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862635389330653184 |
|---|---|
| author | Kashu, A.I. |
| author_facet | Kashu, A.I. |
| citation_txt | Preradicals, closure operators in R-Mod and connection between them / A.I. Kashu // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 86–96. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | For a module category R-Mod the class PR of preradicals and the class CO of closure operators are studied. The relations between these classes are realized by three mappings: Φ : CO → PR and Ψ₁, Ψ₂ : PR → CO. The impact of these mappings on the operations in PR and CO (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa).
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| first_indexed | 2025-11-30T17:04:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-153348 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T17:04:08Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kashu, A.I. 2019-06-14T03:26:34Z 2019-06-14T03:26:34Z 2014 Preradicals, closure operators in R-Mod and connection between them / A.I. Kashu // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 86–96. — Бібліогр.: 6 назв. — англ. 1726-3255 2010 MSC:16D90, 16S90, 06B23. https://nasplib.isofts.kiev.ua/handle/123456789/153348 For a module category R-Mod the class PR of preradicals and the class CO of closure operators are studied. The relations between these classes are realized by three mappings: Φ : CO → PR and Ψ₁, Ψ₂ : PR → CO. The impact of these mappings on the operations in PR and CO (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Preradicals, closure operators in R-Mod and connection between them Article published earlier |
| spellingShingle | Preradicals, closure operators in R-Mod and connection between them Kashu, A.I. |
| title | Preradicals, closure operators in R-Mod and connection between them |
| title_full | Preradicals, closure operators in R-Mod and connection between them |
| title_fullStr | Preradicals, closure operators in R-Mod and connection between them |
| title_full_unstemmed | Preradicals, closure operators in R-Mod and connection between them |
| title_short | Preradicals, closure operators in R-Mod and connection between them |
| title_sort | preradicals, closure operators in r-mod and connection between them |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153348 |
| work_keys_str_mv | AT kashuai preradicalsclosureoperatorsinrmodandconnectionbetweenthem |