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On existence of PIexponents of unital algebras
Repovš, Dušan
(
Author
),
Zaicev, Mikhail
(
Author
)
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Abstract
We construct a family of unital nonassociative 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 PIexponent of codimension growth of algebra ▫$T_\alpha$▫ does not exist for any ▫$\alpha > 2$▫. This is the first example of a unital algebra whose PIexponent does not exist.
Language:
English
Keywords:
polynomial identities
,
exponential codimension growth
,
PIexponent
,
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. 853859
Numbering:
Vol. 28, no. 2
UDC:
512.552
ISSN on article:
26881594
DOI:
10.3934/era.2020044
COBISS.SIID:
20166147
Views:
241
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:
26881594
COBISS.SIID:
20165635
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