On existence of PI-exponents of unital algebras

Dušan D. Repovš, ,Faculty of Mathematics and Physics, University of Ljubljana, & Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia, Mikhail V. Zaicev, ,Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, 119992 Moscow, Russia
2020 Electronic Research Archive  
We construct a family of unital non-associative algebras {T_α| 2<α∈R} such that exp(T_α)=2, whereas α 2. This is the first example of a unital algebra whose PI-exponent does not exist.
doi:10.3934/era.2020044 fatcat:iwlxhjsntfhkhoxql72mhi2pwy