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Fundam. Prikl. Mat., 2004, Volume 10, Issue 3, Pages 157–180 (Mi fpm776)  

This article is cited in 1 scientific paper (total in 1 paper)

Varieties of two-step solvable algebras of type $(\gamma,\delta)$

S. V. Platonova

Ryazan State Pedagogical University

Abstract: The structure of the set of all nonnilpotent subvarieties of the variety of two-step solvable algebras of type $(\gamma,\delta)$ is studied. An additive basis of a free metabelian $(\gamma,\delta)$-algebra is constructed. It is proved that any identity in a nonnilpotent metabelian $(\gamma,\delta)$-algebra of degree at least 6 is a consequence of four defining relations.

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English version:
Journal of Mathematical Sciences (New York), 2006, 139:4, 6762–6779

Bibliographic databases:

UDC: 512.554.5

Citation: S. V. Platonova, “Varieties of two-step solvable algebras of type $(\gamma,\delta)$”, Fundam. Prikl. Mat., 10:3 (2004), 157–180; J. Math. Sci., 139:4 (2006), 6762–6779

Citation in format AMSBIB
\Bibitem{Pla04}
\by S.~V.~Platonova
\paper Varieties of two-step solvable algebras of type $(\gamma,\delta)$
\jour Fundam. Prikl. Mat.
\yr 2004
\vol 10
\issue 3
\pages 157--180
\mathnet{http://mi.mathnet.ru/fpm776}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2123348}
\zmath{https://zbmath.org/?q=an:1072.17017}
\elib{http://elibrary.ru/item.asp?id=9068314}
\transl
\jour J. Math. Sci.
\yr 2006
\vol 139
\issue 4
\pages 6762--6779
\crossref{https://doi.org/10.1007/s10958-006-0389-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750502236}


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    This publication is cited in the following articles:
    1. Kuz'min A., “on the Topological Rank of the Variety of Right Alternative Metabelian Lie-Nilpotent Algebras”, J. Algebra. Appl., 14:10 (2015), 1550144  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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