On class of nilpotency of obstruction to embeddability of algebras satisfying Capelli identities

In a finitely generated algebra $L$ satisfying Capelli identities of order $n+1$ over an arbitrary field there exists a nilpotent ideal $I$ such that the class of nilpotency of the ideal $I$ is not greater than $n$ and the quotient algebra $L/I$ is embeddable. It is shown that this bound of class of nilpotency of obstruction (ideal $I$) in the class of algebras of finite signature cannot be improved.