ABSTRACT
In this paper, we first found a magmatic (i.e., absolutely non-associative) Gröbner-Shirshov basis of a free Gelfand-Dorfman-Novikov algebra GDN(X) such that the corresponding set of irreducible magmatic words is the Dzhumadildaev-Löfwall linear basis of the GDN(X). Then, we prove a Composition-Diamond lemma for right ideals of a free right Leibniz algebra Lei(X).
Acknowledgments
We are deeply indebted to the referee for the useful and detailed comments, because with the help of them our paper got much improvement. Especially, now, the Section 4 is due to the referee.