On existence of PI-exponents of codimension growth

Mikhail Zaicev

doi:10.3934/era.2014.21.113

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

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On existence of PI-exponents of codimension growth

Mikhail Zaicev^1,

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

Received: December 31, 2013

Revised: February 28, 2014

Published: December 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 16R10; Secondary: 16P90.

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