On existence of PI-exponents of unital algebras

Repovš, Dušan (author), Zaicev, Mikhail V. (author)

We construct a family of unital non-associative algebras ▫$\{ T_\alpha | 2 < \alpha \in \mathbb{R} \}$▫ such that ▫$\underline{exp}(T_\alpha) = 2$▫, whereas ▫$\alpha \le \overline{exp} (T_\alpha) \le \alpha + 1$▫. In particular, it follows that ordinary PI-exponent of codimension growth of algebra ▫$T_\alpha$▫ does not exist for any ▫$\alpha > 2$▫. This is the first example of a unital algebra whose PI-exponent does not exist.

• Language: English
• Keywords: polynomial identities, exponential codimension growth, PI-exponent, unital algebra, numerical invariant
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 853-859
• Numbering: Vol. 28, no. 2
• PID: 20.500.12556/RUL-117020
• UDC: 512.552
• ISSN on article: 2688-1594
• DOI: 10.3934/era.2020044
• COBISS.SI-ID: 20166147
• Publication date in RUL: 19.06.2020

Record is a part of a journal

• Title: Electronic research archive
• Shortened title: Electron. res. arch.
• Publisher: American institute of mathematical sciences
• ISSN: 2688-1594
• COBISS.SI-ID: 20165635