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Matematicheskie Zametki, 2006, Volume 80, Issue 3, Pages 413–420
DOI: https://doi.org/10.4213/mzm2827 (Mi mzm2827) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Structure of finitely generated commutative alternative algebras and special Moufang loops

S. V. Pchelintsev

Finance Academy under the Government of the Russian Federation
Full-text PDF (414 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm2827
Abstract: It is proved that the commutator ideal of the multiplication algebra of a free commutative alternative algebra of rank n is nilpotent of index n−1. As a corollary to this fact, the Bruck theorem for special commutative Moufang loops is derived.
Keywords: commutative Moufang loop, central nilpotency, alternative algebra, special Moufang loop.
Received: 17.05.2005
Revised: 12.01.2006
English version:
Mathematical Notes, 2006, Volume 80, Issue 3, Pages 396–402
DOI: https://doi.org/10.1007/s11006-006-0152-1
Bibliographic databases:
UDC: 512.554.5
Language: Russian
Citation: S. V. Pchelintsev, “Structure of finitely generated commutative alternative algebras and special Moufang loops”, Mat. Zametki, 80:3 (2006), 413–420; Math. Notes, 80:3 (2006), 396–402
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm2827
  • https://www.mathnet.ru/eng/mzm/v80/i3/p413
    • This publication is cited in the following 3 articles:
    1. Glizburg V., Pchelintsev S., “Some Finitely Generated Associative Algebras With a Lie Nilpotency Identity”, J. Algebra. Appl., 20:07 (2021), 2150112  crossref  mathscinet  isi
    2. Sergey V. Pchelintsev, “Proper identities of finitely generated commutative alternative algebras”, Journal of Algebra, 470 (2017), 425  crossref
    3. Grishkov A.N., Shestakov I.P., “Commutative Moufang loops and alternative algebras”, J. Algebra, 333:1 (2011), 1–13  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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