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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 2(6), Pages 179–203 (Mi msb2381)  

This article is cited in 9 scientific papers (total in 9 papers)

Varieties of algebras that are solvable of index 2

S. V. Pchelintsev


Abstract: Let $\mathfrak M$ be one of the varieties $\operatorname{Alt}_2$, $(-1,1)_2$, $\operatorname{Malc}_2$ or $\operatorname{Jord}_2$ and let $\mathscr M$ be the set of all non-nilpotent subvarieties of $\mathfrak M$. This set is provided in a natural way with a certain topology. A characterization of $\mathfrak M$ is given in terms of the corresponding structure on $\mathscr M$.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:2, 159–180

Bibliographic databases:

UDC: 519.48
MSC: 17D05, 17A30, 17D10, 17C05
Received: 07.02.1980

Citation: S. V. Pchelintsev, “Varieties of algebras that are solvable of index 2”, Mat. Sb. (N.S.), 115(157):2(6) (1981), 179–203; Math. USSR-Sb., 43:2 (1982), 159–180

Citation in format AMSBIB
\Bibitem{Pch81}
\by S.~V.~Pchelintsev
\paper Varieties of algebras that are solvable of index~2
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 2(6)
\pages 179--203
\mathnet{http://mi.mathnet.ru/msb2381}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=622144}
\zmath{https://zbmath.org/?q=an:0487.17010|0461.17002}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 2
\pages 159--180
\crossref{https://doi.org/10.1070/SM1982v043n02ABEH002442}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Pchelintsev, “Varieties of solvable index-two alternative algebras over a field of characteristic three”, Math. Notes, 66:4 (1999), 455–463  mathnet  crossref  crossref  mathscinet  isi
    2. S. V. Pchelintsev, “An almost Spechtian variety of alternative algebras over a field of characteristic 3”, Sb. Math., 191:6 (2000), 909–925  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. V. Badeev, “Mnogoobrazie $\mathbf N_3\mathbf N_2$ kommutativnykh alternativnykh nil-algebr indeksa 3 nad polem kharakteristiki 3”, Fundament. i prikl. matem., 8:2 (2002), 335–356  mathnet  mathscinet  zmath
    4. S. V. Pchelintsev, “Speciality of Metabelian Mal"tsev Algebras”, Math. Notes, 74:2 (2003), 245–254  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. S. V. Platonova, “Varieties of two-step solvable algebras of type $(\gamma,\delta)$”, J. Math. Sci., 139:4 (2006), 6762–6779  mathnet  crossref  mathscinet  zmath  elib
    6. A. N. Vaulin, “On one variety of alternative algebras”, J. Math. Sci., 140:2 (2007), 191–199  mathnet  crossref  mathscinet  zmath  elib  elib
    7. S. V. Platonova, “Varieties of Two-Step Solvable Algebras of Type (1,1)”, Math. Notes, 76:3 (2004), 379–388  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. S. V. Pchelintsev, “On identities of right alternative metabelian Grassmann algebras”, J. Math. Sci., 154:2 (2008), 230–248  mathnet  crossref  mathscinet  zmath  elib  elib
    9. Alexey Kuz'min, “Nonfinitely Based Varieties of Right Alternative Metabelian Algebras”, Communications in Algebra, 43:8 (2015), 3169  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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