Structure and representation of nonassociative algebras

Note on moufang-noether currents

“…Similar commutation relations are known from the theory of alternative algebras [10]. This is due to the fact that the commutator algebras of alternative algebras are the Mal'tsev algebras.…”

SOLVABILITY OF COMMUTATIVE RIGHT-NILALGEBRAS SATISFYING (b(aa))a = b((aa)a)

“…Since W 2 = 0, we have that A/W and W are solvable. Therefore, from Schafer [3] (Proposition 2.2, p.18), we get that A is solvable, which proves Theorem 5. The proof of Zelmanov and Skosyrskii [5] uses characteristic 6 = 2, 3, 5.…”

On the semisimplicity of the algebra associated to a polarized algebraic variety

“…Theorem 2 follows from the next general theorem (Cf, [3]). But in our case the trace form is positive definite so the proof of Theorem 2 is easy as we shall see in §3.…”