Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators)

• 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; lattice of submodules; dense submodule; closed submodule; 16D90; 16S90; 06B23
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/744
• Journal Title: Algebra and Discrete Mathematics

In this work the closure operators of a category of modules \(R\)-Mod are studied. Every closure operator \(C\) of \(R\)-Mod defines two functions \( \mathcal{F}_1^{C}\) and \(\mathcal{F}_2^{C}\), which  in every module \(M\) distinguish the set of \(C\)-dense submodules  \(\mathcal{F}_1^{C}(M)\) an...