Abstract: | We prove that the isotopes of the alternative monster and the Skosyrsky algebra satisfy the identity Пi=14 xi, yi] = 0. Hence, the algebras themselves satisfy the identity Пi=14 (c, xi, yi) = 0. We also show that none of the identities Пi=1n(c, xi, yi) = 0 holds in all commutative alternative nil-algebras of index 3. Thus, we refute the Grishkov–Shestakov hypothesis about the structure of the free finitely generated commutative alternative nil-algebras of index 3. |