Nilpotent ideals of a free alternative algebra (Q795157)

Let \(\Phi\) be an associative commutative ring with identity and containing 1/6. In a free alternative \(\Phi\)-algebra A with \(k\geq 6\) free generators the author constructs a trivial ideal, which is not contained in the associative center of A. The author also constructs a completely characteristic non-zero nilpotent ideal of index \(n\leq 3\) in the free alternative algebra with \(k\geq 5\) free generators.