Preradicals, closure operators in \(R\)-Mod and connection between them

• Date: 2018
• Main Author: Kashu, A. I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: ring; module; lattice; preradical; closure operator; product ( coproduct) of closure operators; 16D90; 16S90; 06B23
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1048
• Journal Title: Algebra and Discrete Mathematics

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...