Ideally finite Leibniz algebras

• Date: 2023
• Main Authors: Kurdachenko, L. A., Subbotin, I. Ya.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: Leibniz algebra; ideally finite algebras; Lie algebra; breadth of elements; 17A32; 17A31
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2139
• Journal Title: Algebra and Discrete Mathematics

The aim of this paper is to consider Leibniz algebras, whose principal ideals are finite dimensional. We prove that the derived ideal of \(L\) has finite dimension if every principal ideal of a Leibniz algebra \(L\) has dimension at most \(b\), where \(b\) is a fixed positive integer.