Leibniz rings: some basic and structural results

2025/08/24 by Kurdachenko, L. A., Pypka, O. O., Semko, M. M.
#FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.17319

Abstract

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.

Citations

• On the algebra of derivations of some low-dimensional Leibniz algebras
• On the automorphism groups of some Leibniz algebras
• Relationships between the generalized central series of Leibniz algebras
• On the endomorphisms and derivations of some Leibniz algebras
• Schunck classes of soluble Leibniz algebras

Related

• Some Properties of Posynomial Rings
• On structures of the ring of arithmetical functions: prime ideals and beyond
• Peirce decompositions, idempotents and rings
• Rings involving idempotents, units and nilpotent elements
• Structure theorems for AP rings