Mal'tsev-admissible right alternative nil algebras of bounded index (Q1920800)

A right alternative algebra \(A\) is called Malcev admissible if its associated commutator algebra \(A^{(-)}\) is a Malcev algebra. The author extends two well-known results for alternative algebras, that are due to Zhevlakov and Shirshov, by proving the following: Over a field of characteristic 0, a Malcev-admissible right alternative nil algebra of bounded index is both solvable and locally nilpotent.