Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2017, Number 6, Pages 15–20 (Mi vmumm105)  
This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Growth of codimensions of metabelian algebras

M. V. Zaicev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (318 kB) Citations (4)
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Abstract: We consider numerical invariants of identities of nonassociative algebras. We prove that codimension sequence of any finitely generated metabelian algebra has exponentially bounded codimension growth. It is shown that the upper PI-exponent increases at most to 1 after adjoining an external unit. For two-step left-nilpotent algebras it is proved that the lower PI-exponent increases at least to 1.
Key words: identities, codimensions, metabelian algebras, PI-exponent.
Funding agency Grant number
Russian Science Foundation 16-11-10013
Received: 15.03.2017
English version:
Moscow University Mathematics Bulletin, 2017, Volume 72, Issue 6, Pages 233–237
DOI: https://doi.org/10.3103/S0027132217060031
Bibliographic databases:
Document Type: Article
UDC: 512.572
Language: Russian
Citation: M. V. Zaicev, “Growth of codimensions of metabelian algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 6, 15–20; Moscow University Mathematics Bulletin, 72:6 (2017), 233–237
Citation in format AMSBIB
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\pages 15--20
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    • This publication is cited in the following 4 articles:
    1. M. V. Zaicev, S. P. Mishchenko, “Codimension Sequences and their Asymptotic Behavior”, J Math Sci, 257:6 (2021), 825  crossref
    2. Dušan D. Repovš, Mikhail V. Zaicev, “On existence of PI-exponents of unital algebras”, era, 28:2 (2020), 853  crossref
    3. M. V. Zaicev, D. D. Repovš, “Combinatorics on binary words and codimensions of identities in left nilpotent algebras”, Algebra and Logic, 58:1 (2019), 23–35  mathnet  crossref  crossref  isi
    4. M. V. Zaitsev, S. P. Mischenko, “Posledovatelnosti korazmernostei tozhdestv i ikh asimptoticheskoe povedenie”, Fundament. i prikl. matem., 22:4 (2019), 115–127  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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