On the structure of some Leibniz rings

• Date: 2025
• Main Authors: Kurdachenko, Leonid A., Pypka, Oleksandr O., Semko, Mykola M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: Leibniz ring; Lie ring; Leibniz algebra; additive group of Leibniz ring; 17A32; 17A60; 17A99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2426
• Journal Title: Algebra and Discrete Mathematics

In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtained illustrate a significant difference between the classes of Leibniz rings and Lie rings.