Abstract
<p style='text-indent:20px;'>We construct a family of unital non-associative algebras <inline-formula><tex-math id="M1">$ \{T_\alpha\vert\; 2&lt;\alpha\in\mathbb R\} $</tex-math></inline-formula> such that <inline-formula><tex-math id="M2">$ \underline{exp}(T_\alpha) = 2 $</tex-math></inline-formula>, whereas <inline-formula><tex-math id="M3">$ \alpha\le\overline{exp}(T_\alpha)\le\alpha+1 $</tex-math></inline-formula>. In particular, it follows that ordinary PI-exponent of codimension growth of algebra <inline-formula><tex-math id="M4">$ T_\alpha $</tex-math></inline-formula> does not exist for any <inline-formula><tex-math id="M5">$ \alpha&gt; 2 $</tex-math></inline-formula>. This is the first example of a unital algebra whose PI-exponent does not exist.</p>
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
