### Electronic Research Archive

2020, Issue 2: 853-859. doi: 10.3934/era.2020044

# On existence of PI-exponents of unital algebras

• Primary: 16R10; Secondary: 16P90

• We construct a family of unital non-associative algebras $\{T_\alpha\vert\; 2<\alpha\in\mathbb R\}$ 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.

Citation: Dušan D. Repovš, Mikhail V. Zaicev. On existence of PI-exponents of unital algebras[J]. Electronic Research Archive, 2020, 28(2): 853-859. doi: 10.3934/era.2020044

### Related Papers:

• We construct a family of unital non-associative algebras $\{T_\alpha\vert\; 2<\alpha\in\mathbb R\}$ 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.

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