Preradicals, closure operators in \(R\)-Mod and connection between them
For a module category \(R\)-Mod the class \(\mathbb{PR}\) of preradicals and the class \(\,\mathbb{CO} \,\) of closure operators are studied. The relations between these classes are realized by three mappings: \(\Phi : \mathbb{CO} \to \mathbb{PR}\) and \(\,\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO...
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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | For a module category \(R\)-Mod the class \(\mathbb{PR}\) of preradicals and the class \(\,\mathbb{CO} \,\) of closure operators are studied. The relations between these classes are realized by three mappings: \(\Phi : \mathbb{CO} \to \mathbb{PR}\) and \(\,\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}\). The impact of these mappings on the operations in \(\mathbb{PR}\) and \(\mathbb{CO}\) (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa). |
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