@article{article_1607238, title={On a variety of Lie-admissible algebras}, journal={International Electronic Journal of Algebra}, volume={37}, pages={1–13}, year={2025}, DOI={10.24330/ieja.1607238}, author={Facchini, Alberto}, keywords={Lie-admissible algebra, pre-Lie algebra, $~$}, abstract={The aim of this paper is to propose the study of a class of Lie-admissible algebras. It is the class (variety) of all the (not-necessarily associative) algebras $M$ over a commutative ring $k$ with identity $1_k$ for which $(x,y,z)=(y,x,z)+(z,y,x)$ for every $x,y,z\in M$. Here $(x,y,z)$ denotes the associator of $M$. We call such algebras algebras of type $\mathcal{V}_2$. Very little is known about these algebras.}, number={37}, publisher={Abdullah HARMANCI}