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On existence of PI-exponents of codimension growth

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  • We construct a family of examples of non-associative algebras $\{R_\alpha \,\vert\, 1<\alpha\in\mathbb R\}$ such that $\underline{\exp}(R_\alpha)=1$, $\overline{\exp}(R_\alpha)=\alpha$. In particular, it follows that for any $R_\alpha$, an ordinary PI-exponent of codimension growth does not exist.
    Mathematics Subject Classification: Primary: 16R10; Secondary: 16P90.

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