Grobner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras

摘要

In this paper, we first found a magmatic (i.e., absolutely non-associative) Grobner-Shirshov basis of a free Gelfand-Dorfman-Novikov algebra GDN(X) such that the corresponding set of irreducible magmatic words is the Dzhumadildaev-Lofwall linear basis of the GDN(X). Then, we prove a Composition-Diamond lemma for right ideals of a free right Leibniz algebra Lei(X).