Geodesic
An independent system of identities for a~variety of mono-Leibniz algebras
Algebra i logika, Tome 49 (2010) no. 2, pp. 175-180.

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We introduce the notion of a mono-Leibniz algebra generalizing the concept of a Leibniz algebra. Namely, an algebra $A$ over a field $K$, $\operatorname{char}K\ne2$, 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 $$ x(xx)=0,\qquad x[(xx)x]=0. $$ Examples of mono-Leibniz algebras are given which show that $W$ is not a Schreier variety.
Keywords: mono-Leibniz algebra, variety, system of identities. 
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A. T. Gainov. An independent system of identities for a~variety of mono-Leibniz algebras. Algebra i logika, Tome 49 (2010) no. 2, pp. 175-180. http://geodesic.mathdoc.fr/item/AL_2010_49_2_a1/

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