Preradicals, closure operators in \(R\)-Mod and connection between them
For a module category \(R\)-Mod the class \(\mathbb{PR}\) of preradicals and the class \(\,\mathbb{CO} \,\) of closure operators are studied. The relations between these classes are realized by three mappings: \(\Phi : \mathbb{CO} \to \mathbb{PR}\) and \(\,\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO...
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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543332701831168 |
|---|---|
| author | Kashu, A. I. |
| author_facet | Kashu, A. I. |
| author_sort | Kashu, A. I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:28:53Z |
| description | For a module category \(R\)-Mod the class \(\mathbb{PR}\) of preradicals and the class \(\,\mathbb{CO} \,\) of closure operators are studied. The relations between these classes are realized by three mappings: \(\Phi : \mathbb{CO} \to \mathbb{PR}\) and \(\,\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}\). The impact of these mappings on the operations in \(\mathbb{PR}\) and \(\mathbb{CO}\) (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). |
| first_indexed | 2026-02-08T07:57:33Z |
| format | Article |
| id | admjournalluguniveduua-article-1048 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:33Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-10482018-04-26T02:28:53Z Preradicals, closure operators in \(R\)-Mod and connection between them Kashu, A. I. ring, module, lattice, preradical, closure operator, product ( coproduct) of closure operators 16D90, 16S90, 06B23 For a module category \(R\)-Mod the class \(\mathbb{PR}\) of preradicals and the class \(\,\mathbb{CO} \,\) of closure operators are studied. The relations between these classes are realized by three mappings: \(\Phi : \mathbb{CO} \to \mathbb{PR}\) and \(\,\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}\). The impact of these mappings on the operations in \(\mathbb{PR}\) and \(\mathbb{CO}\) (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). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048 Algebra and Discrete Mathematics; Vol 18, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048/570 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | ring module lattice preradical closure operator product ( coproduct) of closure operators 16D90 16S90 06B23 Kashu, A. I. Preradicals, closure operators in \(R\)-Mod and connection between them |
| 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 |
| topic | ring module lattice preradical closure operator product ( coproduct) of closure operators 16D90 16S90 06B23 |
| topic_facet | ring module lattice preradical closure operator product ( coproduct) of closure operators 16D90 16S90 06B23 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048 |
| work_keys_str_mv | AT kashuai preradicalsclosureoperatorsinrmodandconnectionbetweenthem |