Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators)
In this work the closure operators of a category of modules \(R\)-Mod are studied. Every closure operator \(C\) of \(R\)-Mod defines two functions \( \mathcal{F}_1^{C}\) and \(\mathcal{F}_2^{C}\), which in every module \(M\) distinguish the set of \(C\)-dense submodules \(\mathcal{F}_1^{C}(M)\) an...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/744 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543359356633088 |
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| author | Kashu, A. I. |
| author_facet | Kashu, A. I. |
| author_sort | Kashu, A. I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T00:55:03Z |
| description | In this work the closure operators of a category of modules \(R\)-Mod are studied. Every closure operator \(C\) of \(R\)-Mod defines two functions \( \mathcal{F}_1^{C}\) and \(\mathcal{F}_2^{C}\), which in every module \(M\) distinguish the set of \(C\)-dense submodules \(\mathcal{F}_1^{C}(M)\) and the set of \(C\)-closed submodules \(\mathcal{F}_2^{C}(M)\). By means of these functions three types of closure operators are described: 1)weakly hereditary; 2)idempotent; 3)weakly hereditary and idempotent. |
| first_indexed | 2026-02-08T07:58:02Z |
| format | Article |
| id | admjournalluguniveduua-article-744 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:02Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7442018-04-26T00:55:03Z Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) Kashu, A. I. ring, module, lattice, preradical, closure operator, lattice of submodules, dense submodule, closed submodule 16D90, 16S90, 06B23 In this work the closure operators of a category of modules \(R\)-Mod are studied. Every closure operator \(C\) of \(R\)-Mod defines two functions \( \mathcal{F}_1^{C}\) and \(\mathcal{F}_2^{C}\), which in every module \(M\) distinguish the set of \(C\)-dense submodules \(\mathcal{F}_1^{C}(M)\) and the set of \(C\)-closed submodules \(\mathcal{F}_2^{C}(M)\). By means of these functions three types of closure operators are described: 1)weakly hereditary; 2)idempotent; 3)weakly hereditary and idempotent. 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/744 Algebra and Discrete Mathematics; Vol 15, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/744/274 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | ring module lattice preradical closure operator lattice of submodules dense submodule closed submodule 16D90 16S90 06B23 Kashu, A. I. Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) |
| title | Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) |
| title_full | Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) |
| title_fullStr | Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) |
| title_full_unstemmed | Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) |
| title_short | Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators) |
| title_sort | closure operators in the categories of modules part i (weakly hereditary and idempotent operators) |
| topic | ring module lattice preradical closure operator lattice of submodules dense submodule closed submodule 16D90 16S90 06B23 |
| topic_facet | ring module lattice preradical closure operator lattice of submodules dense submodule closed submodule 16D90 16S90 06B23 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/744 |
| work_keys_str_mv | AT kashuai closureoperatorsinthecategoriesofmodulespartiweaklyhereditaryandidempotentoperators |