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Matematicheskie Zametki, 2004, Volume 76, Issue 3, Pages 409–419
DOI: https://doi.org/10.4213/mzm117 (Mi mzm117) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Varieties of Two-Step Solvable Algebras of Type (1,1)

S. V. Platonova

Ryazan State Pedagogical University
Full-text PDF (184 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm117
Abstract: The structure of the set of all non-nilpotent subvarieties of the variety of two-step solvable algebras of type (1,1) is studied. An additive basis of a free metabelian (1,1)-algebra is constructed. It is proved that any identity in a non-nilpotent metabelian (1,1)-algebra of degree ⩾6 is a consequence of four defining relations.
Received: 12.02.2003
English version:
Mathematical Notes, 2004, Volume 76, Issue 3, Pages 379–388
DOI: https://doi.org/10.1023/B:MATN.0000043465.59075.88
Bibliographic databases:
UDC: 512.554.5
Language: Russian
Citation: S. V. Platonova, “Varieties of Two-Step Solvable Algebras of Type (1,1)”, Mat. Zametki, 76:3 (2004), 409–419; Math. Notes, 76:3 (2004), 379–388
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    1. Dongsu Kim, Yeobeom Yoon, Jongman Lee, Pedro J. Mago, Kwangho Lee, Heejin Cho, “Design and Implementation of Smart Buildings: A Review of Current Research Trend”, Energies, 15:12 (2022), 4278  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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