An independent system of identities for a variety of mono-Leibniz algebras

We introduce the notion of a mono-Leibniz algebra generalizing the concept of a Leibniz algebra. Namely, an algebra A over a field K, charK ≠ 2, is mono-Leibniz if its one-generated subalgebras each is a Leibniz algebra. It is proved that a variety W of mono-Leibniz algebras over an infinite field K is defined by an independent system of identities such as x(xx) = 0 and x(xx)x] = 0. Examples of mono-Leibniz algebras are given which show that W is not a Schreier variety.