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) ...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/704 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-704 |
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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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T09:53:26Z |
| collection |
OJS |
| language |
English |
| topic |
ring module preradical lattice product of submodules left (right) quotient 16D90 16S90 06B23 |
| 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 |
| topic_facet |
ring module preradical lattice product of submodules left (right) quotient 16D90 16S90 06B23 |
| format |
Article |
| author |
Kashu, A. I. |
| author_facet |
Kashu, A. I. |
| author_sort |
Kashu, A. I. |
| title |
On inverse operations in the lattices of submodules |
| title_short |
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_sort |
on inverse operations in the lattices of submodules |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/704 |
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AT kashuai oninverseoperationsinthelatticesofsubmodules |
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2025-12-02T15:32:11Z |
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2025-12-02T15:32:11Z |
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1850411090568019968 |