Upper bounds for the length of non-associative algebras

We introduce the notion of length for non-associative finite-dimensional unitary algebras and obtain a sharp upper bound for the lengths of algebras belonging to this class. We also put forward a new method of characteristic sequences based on linear algebra technique, which provides an efficient tool for computing the length function in non-associative case. Then we apply the introduced method to obtain an upper bound for the length of an arbitrary locally complex algebra. In the last case the length is bounded in terms of the Fibonacci sequence. We present concrete examples demonstrating the sharpness of our bounds.