**MSC:**- 16S15 Finite generation, finite presentability, normal forms
- 08A05 Structure theory

\N$ is given being equivalent to the possibility to generate ${\cal A}$ by $n$

subalgebras having square zero and all except one of them having dimension 1.

As a corollary under this condition, the algebra can be generated by two

subalgebras with square zero such that one of them has dimension 1 or 2 in

dependence on whether $n$ is even or odd. In the case of the algebra ${\cal

B}(E)$ of all continuous linear operators on a Banach space $E$, the

condition is fulfilled if and only if $E$ is the $n$th power $E = E_0^n$ of a Banach

space $E_0$. This way by elementary considerations, not only a problem

considered by W.\,{\. Z}elazko and afterwards by P.\,{\v S}emrl is finished

but also completely extended to arbitrary simple algebras with unit.