On existence of PI-exponents of unital algebrasRepovš, Dušan (Avtor) Zaicev, Mikhail (Avtor) polynomial identitiesexponential codimension growthPI-exponentunital algebranumerical invariantWe 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, it follows that ordinary PI-exponent of codimension growth of algebra ▫$T_\alpha$▫ does not exist for any ▫$\alpha > 2$▫. This is the first example of a unital algebra whose PI-exponent does not exist.20202020-06-19 11:34:37Članek v reviji117020sl