On existence of PI-exponents of unital algebras

Dušan Repovš (Author), Mikhail Zaicev (Author)

Abstract

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.

Keywords

polynomial identities;exponential codimension growth;PI-exponent;unital algebra;numerical invariant;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.552
COBISS:	20166147
ISSN:	2688-1594
Views:	518
Downloads:	185
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Type (COBISS):	Article
Pages:	str. 853-859
Volume:	ǂVol. ǂ28
Issue:	ǂno. ǂ2
Chronology:	June 2020
DOI:	10.3934/era.2020044
ID:	11852109