论文标题
关于Unital代数的Pi exponents
On existence of PI-exponents of unital algebras
论文作者
论文摘要
我们构建了一个Unital非相关代数$ \ {t_α\ vert〜2 <α\ in \ Mathbb r \} $，这样$ \ useverline {exp}（t_α）= 2 $，而$ \ useverline {exp} = 2 $特别是，因此，对于任何$α> 2 $，代数$t_α$的consimension增长的普通Pi epponent均不存在。这是一个Unital代数的第一个示例，其pi exponent不存在。
We construct a family of unital non-associative algebras $\{T_α\vert~ 2<α\in\mathbb R\}$ such that $\underline{exp}(T_α)=2$, whereas $α\le\overline{exp}(T_α)\leα+1$. In particular, it follows that ordinary PI-exponent of codimension growth of algebra $T_α$ does not exist for any $α> 2$. This is the first example of a unital algebra whose PI-exponent does not exist.
