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On existence of PI-exponents of unital algebras
Repovš, Dušan (Author), Zaicev, Mikhail (Author)

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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.

Language:English
Keywords:polynomial identities, exponential codimension growth, PI-exponent, unital algebra, numerical invariant
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2020
Number of pages:str. 853-859
Numbering:Vol. 28, no. 2
UDC:512.552
ISSN on article:2688-1594
DOI:10.3934/era.2020044 Link is opened in a new window
COBISS.SI-ID:20166147 Link is opened in a new window
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Downloads:104
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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 This link opens in a new window

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