On lattices, modules and groups with many uniform elements

• Date: 2018
• Main Author: Krempa, Jan
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: uniform element; locally uniform lattice; lattice of subgroups; lattice of submodules; 06C99; 16S90; 20E15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/981
• Journal Title: Algebra and Discrete Mathematics

The uniform dimension, also known as Goldie dimension, can be defined and used not only in the class of modules, but also in large classes of lattices and groups. For considering this dimension it is necessary to involve uniform elements. In this paper we are going to discuss properties of lattices...