Nil-algebras and infinite groups

We simplify our construction of nil-algebras by proving, for any integer d ≥ 2 and over any field , that there exists a residually nilpotent, nonnilpotent nil-algebra over generated by d elements. As a consequence, we obtain similar results for nonassociative algebras and groups. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 3, pp. 189–200, 2005.