Preradicals and characteristic submodules: connections and operations
For an arbitrary module \(M\in R\)-Mod the relation between the lattice \(\mathbf{L}^{ch}(_{R}M)\) of characteristic (fully invariant) submodules of \(M\) and big lattice \(R\)-pr of preradicals of \(R\)-Mod is studied. Some isomorphic images of \(\mathbf{L}^{ch}(_{R}M)\) in \(R\)-pr are construct...
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/631 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543311779594240 |
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| author | Kashu, A. I. |
| author_facet | Kashu, A. I. |
| author_sort | Kashu, A. I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:11:25Z |
| description | For an arbitrary module \(M\in R\)-Mod the relation between the lattice \(\mathbf{L}^{ch}(_{R}M)\) of characteristic (fully invariant) submodules of \(M\) and big lattice \(R\)-pr of preradicals of \(R\)-Mod is studied. Some isomorphic images of \(\mathbf{L}^{ch}(_{R}M)\) in \(R\)-pr are constructed. Using the product and coproduct in \(R\)-pr four operations in the lattice \(\mathbf{L}^{ch}(_{R}M)\) are defined. Some properties of these operations are shown and their relations with the lattice operations in \(\mathbf{L}^{ch}(_{R}M)\) are investigated. As application the case \(_{R} M = _{R} R \) is mentioned, when \(\mathbf{L}^{ch}(_{R}R)\) is the lattice of two-sided ideals of ring \(R\). |
| first_indexed | 2025-12-02T15:44:42Z |
| format | Article |
| id | admjournalluguniveduua-article-631 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:44:42Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6312018-04-04T09:11:25Z Preradicals and characteristic submodules: connections and operations Kashu, A. I. preradical, lattice, characteristic submodule, product (coproduct) of preradicals 16D90, 16S90, 06B23 For an arbitrary module \(M\in R\)-Mod the relation between the lattice \(\mathbf{L}^{ch}(_{R}M)\) of characteristic (fully invariant) submodules of \(M\) and big lattice \(R\)-pr of preradicals of \(R\)-Mod is studied. Some isomorphic images of \(\mathbf{L}^{ch}(_{R}M)\) in \(R\)-pr are constructed. Using the product and coproduct in \(R\)-pr four operations in the lattice \(\mathbf{L}^{ch}(_{R}M)\) are defined. Some properties of these operations are shown and their relations with the lattice operations in \(\mathbf{L}^{ch}(_{R}M)\) are investigated. As application the case \(_{R} M = _{R} R \) is mentioned, when \(\mathbf{L}^{ch}(_{R}R)\) is the lattice of two-sided ideals of ring \(R\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/631 Algebra and Discrete Mathematics; Vol 9, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/631/165 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | preradical lattice characteristic submodule product (coproduct) of preradicals 16D90 16S90 06B23 Kashu, A. I. Preradicals and characteristic submodules: connections and operations |
| title | 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_short | Preradicals and characteristic submodules: connections and operations |
| title_sort | preradicals and characteristic submodules: connections and operations |
| topic | preradical lattice characteristic submodule product (coproduct) of preradicals 16D90 16S90 06B23 |
| topic_facet | preradical lattice characteristic submodule product (coproduct) of preradicals 16D90 16S90 06B23 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/631 |
| work_keys_str_mv | AT kashuai preradicalsandcharacteristicsubmodulesconnectionsandoperations |