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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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| 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| Summary: | 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 \(R\). |
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