On the structure of Leibniz algebras whose subalgebras are ideals or core-free

Abstract

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. A subalgebra S of a Leibniz algebra L is called a core-free, if S does not include a non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.