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Composition Diamond lemma for Lie algebra over a field $F$ has already been investigated in several papers :

L.Bokut and Y.Q.Chen Groebner-Shirshov bases for Lie algebras

and

A.I Shirshov, Some algorithmic problems for Lie algebras

I am looking for a paper including composition lemma for the case of Leibniz algebras? I appreciate your comments and your time in advance.

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  • $\begingroup$ Even if it isn't specifically applicable , I recommend George Bergman's article on Newman's Diamond Lemma. His presentation shows the wide generality of the Lemma. Gerhard "Other Perspectives Can Be Useful" Paseman, 2016.07.24. $\endgroup$
    – Gerhard Paseman
    Commented Jul 24, 2016 at 18:56
  • $\begingroup$ Thank you very much for your comment, the exact name of article is "on Newman's Diamond Lemma" ? $\endgroup$
    – user118746
    Commented Jul 24, 2016 at 21:54
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    $\begingroup$ @user118746, I think that it is "The diamond lemma for ring theory" (MR). $\endgroup$
    – LSpice
    Commented Jul 24, 2016 at 23:14

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