Geodesic
Levitzki Radical for certain Varieties
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1005-1011

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a nonassociative algebra. We let An denote the subalgebra generated by all products of n elements from A. Inductively we define A (0) = A and A (n+1) = (A(n) )2. We say that A is nilpotent if, for some n, An = {0}. A is solvable if A(n) = {0} for some n. An algebra is locally nilpotent (locally solvable) if each finitely generated subalgebra is nilpotent (solvable). In this paper will always be some variety of algebras defined by a set of homogeneous identities. We say that local nilpotence is a radical property in if each contains a maximal locally nilpotent ideal L and A/L has no non-zero locally nilpotent ideals. The ideal L is then called the Levitzki radical of A. 
Pokrass, David. Levitzki Radical for certain Varieties. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1005-1011. doi: 10.4153/CJM-1979-092-0
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