On inverse operations in the lattices of submodules
In the lattice \(\mathbf{L}(_{R}M)\) of submodules of an arbitrary left \(R\)-module \(_R M\) four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for \(\alpha\)-product and \(\omega\)-coproduct) ...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/704 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543264543342592 |
|---|---|
| author | Kashu, A. I. |
| author_facet | Kashu, A. I. |
| author_sort | Kashu, A. I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:53:26Z |
| description | In the lattice \(\mathbf{L}(_{R}M)\) of submodules of an arbitrary left \(R\)-module \(_R M\) four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for \(\alpha\)-product and \(\omega\)-coproduct) are defined and studied. Some properties of left quotient with respect to \(\alpha\)-product and right quotient with respect to \(\omega\)-coproduct are shown, as well as their relations with the lattice operations in \(\mathbf{L}(_{R}M)\) (sum and intersection of submodules). The particular case \(_{R}M=_{R}R\) of the lattice \(\mathbf{L}(_{R}R)\) of left ideals of the ring \(R\) is specified. |
| first_indexed | 2025-12-02T15:32:11Z |
| format | Article |
| id | admjournalluguniveduua-article-704 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:32:11Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7042018-04-04T09:53:26Z On inverse operations in the lattices of submodules Kashu, A. I. ring, module, preradical, lattice, product of submodules, left (right) quotient 16D90, 16S90, 06B23 In the lattice \(\mathbf{L}(_{R}M)\) of submodules of an arbitrary left \(R\)-module \(_R M\) four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for \(\alpha\)-product and \(\omega\)-coproduct) are defined and studied. Some properties of left quotient with respect to \(\alpha\)-product and right quotient with respect to \(\omega\)-coproduct are shown, as well as their relations with the lattice operations in \(\mathbf{L}(_{R}M)\) (sum and intersection of submodules). The particular case \(_{R}M=_{R}R\) of the lattice \(\mathbf{L}(_{R}R)\) of left ideals of the ring \(R\) is specified. 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/704 Algebra and Discrete Mathematics; Vol 13, No 2 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/704/237 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | ring module preradical lattice product of submodules left (right) quotient 16D90 16S90 06B23 Kashu, A. I. On inverse operations in the lattices of submodules |
| title | On inverse operations in the lattices of submodules |
| title_full | On inverse operations in the lattices of submodules |
| title_fullStr | On inverse operations in the lattices of submodules |
| title_full_unstemmed | On inverse operations in the lattices of submodules |
| title_short | On inverse operations in the lattices of submodules |
| title_sort | on inverse operations in the lattices of submodules |
| topic | ring module preradical lattice product of submodules left (right) quotient 16D90 16S90 06B23 |
| topic_facet | ring module preradical lattice product of submodules left (right) quotient 16D90 16S90 06B23 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/704 |
| work_keys_str_mv | AT kashuai oninverseoperationsinthelatticesofsubmodules |