On existence of PI-exponents of unital algebras

Dušan D. Repovš, Mikhail V. Zaicev

We construct a family of unital non-associative algebras $\{T_{\alpha }|2<\alpha \in \mathbb{R}\}$ such that $\underline{exp}(T_{\alpha })=2$, whereas $\alpha \le \overline{exp}(T_{\alpha })\le \alpha +1$. In particular,…