# American Institute of Mathematical Sciences

2014, 21: 113-119. doi: 10.3934/era.2014.21.113

## On existence of PI-exponents of codimension growth

 1 Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russian Federation

Received  January 2014 Revised  March 2014 Published  June 2014

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.
Citation: Mikhail Zaicev. On existence of PI-exponents of codimension growth. Electronic Research Announcements, 2014, 21: 113-119. doi: 10.3934/era.2014.21.113
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