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...
Saved in:
| Date: | 2018 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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). |
|---|