On existence of PI-exponents of unital algebras

Repovš, Dušan (avtor), Zaicev, Mikhail (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: polynomial identities, exponential codimension growth, PI-exponent, unital algebra, numerical invariant
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2020
• Št. strani: Str. 853-859
• Številčenje: Vol. 28, no. 2
• PID: 20.500.12556/RUL-117020
• UDK: 512.552
• ISSN pri članku: 2688-1594
• DOI: 10.3934/era.2020044
• COBISS.SI-ID: 20166147
• Datum objave v RUL: 19.06.2020

Gradivo je del revije

• Naslov: Electronic research archive
• Skrajšan naslov: Electron. res. arch.
• Založnik: American institute of mathematical sciences
• ISSN: 2688-1594
• COBISS.SI-ID: 20165635