Abstract
Let $L$ be a finitely generated free Lie $p$-algebra and $\langle a\rangle$ an ideal generated by $a\in L$. It is proved that $L/\langle a \rangle$ is free if and only if $\langle a\rangle$ is primitive (i.e. $a$ belongs to some set of free generators of $L$). Earlier analogues theorems were proved for some objects, for example, for groups, Lie algebras, free algebras and so on.
Citation
G. Rakviashvili. "Primitive elements of free Lie $p$-algebras." Tbilisi Math. J. 8 (2) 35 - 40, December 2015. https://doi.org/10.1515/tmj-2015-0008
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