20.500.12556/RUL-117020 On existence of PI-exponents of unital algebras 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, 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. polynomial identities exponential codimension growth PI-exponent unital algebra numerical invariant true false true Angleški jezik Angleški jezik Članek v reviji 2020-06-19 11:34:37 2020-06-19 11:34:38 2022-08-29 03:40:33 0000-00-00 00:00:00 2020 0 0 Str. 853-859 no. 2 Vol. 28 June 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.552 2688-1594 10.3934/era.2020044 20166147 20165635 RAZ_Repovs_Dusan_2020.pdf RAZ_Repovs_Dusan_2020.pdf 1 57B9F58621DF6D28EFCC4C37F30CBDD8 d4db5486f061e695f17b56387d6df2b4a17bde68cf16f7898dc58a9665d17fc6 1651c798-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=130847 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0