On analogs of some group-theoretic concepts and results for Leibniz algebras - Kurdachenko, L.A.; Subbotin, I.Ya.; Semko, N.N. (Reports of the National Academy of Sciences of Ukraine, 2018)
An algebra L over a field F is said to be a Leibniz algebra (more precisely a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] – [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras. We consider some classes of generalized nilpotent Leibniz algebras (hypercentral, locally nilpotent algebras, and algebras with the idealizer condition) and show their some basic properties.