Email this article Critical vector spaces and extremal $L$ -varieties
- Authors: Kislitsin A.V.1
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Affiliations:
- Altai State Pedagogical University, Barnaul, Russia
- Issue: Vol 217, No 1 (2026)
- Pages: 89-97
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/378950
- DOI: https://doi.org/10.4213/sm10232
- ID: 378950
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Abstract
An example of an almost commutative, almost Engel and almost finitely based $L$ -variety is presented that is generated by a multiplicative vector space distinct from its enveloping algebra. Also, an example of a critical multiplicative vector space is constructed that is not a linear algebra.
About the authors
Alexey Vladimirovich Kislitsin
Altai State Pedagogical University, Barnaul, Russia
Email: kislitsin@altspu.ru
ORCID iD: 0000-0002-2734-102X
SPIN-code: 6448-0484
Scopus Author ID: 55897208600
ResearcherId: C-5358-2016
Candidate of physico-mathematical sciences, Associate professor
References
- O. B. Finogenova, “Characterizing non-matrix properties of varieties of algebras in the language of forbidden objects”, Serdica Math. J., 38:1-3 (2012), 473–496
- Yu. N. Mal'cev, “Just non commutative varieties of operator algebras and rings with some conditions on nilpotent elements”, Tamkang J. Math., 27:1 (1996), 59–65
- M. F. Newman, “Just non-finitely-based varieties of groups”, Bull. Austral. Math. Soc., 4:3 (1971), 343–348
- V. Drensky, “Weak polynomial identities and their applications”, Commun. Math., 29:2 (2021), 291–324
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