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Algebra Logika, 2005, Volume 44, Number 3, Pages 269–304 (Mi al112)  

This article is cited in 11 scientific papers (total in 11 papers)

Bounded Algebraic Geometry over a Free Lie Algebra

E. Yu. Daniyarova, V. N. Remeslennikov

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: Bounded algebraic sets over a free Lie algebra $F$ over a field $k$ are classified in three equivalent languages: (1) in terms of algebraic sets; (2) in terms of radicals of algebraic sets; (3) in terms of coordinate algebras of algebraic sets.

Keywords: arithmetic hierarchy, Rogers semilattice, elementary theory

Full text: PDF file (320 kB)
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English version:
Algebra and Logic, 2005, 44:3, 148–167

Bibliographic databases:

UDC: 512.55+512.7
Received: 20.04.2004
Revised: 06.12.2004

Citation: E. Yu. Daniyarova, V. N. Remeslennikov, “Bounded Algebraic Geometry over a Free Lie Algebra”, Algebra Logika, 44:3 (2005), 269–304; Algebra and Logic, 44:3 (2005), 148–167

Citation in format AMSBIB
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\by E.~Yu.~Daniyarova, V.~N.~Remeslennikov
\paper Bounded Algebraic Geometry over a~Free Lie~Algebra
\jour Algebra Logika
\yr 2005
\vol 44
\issue 3
\pages 269--304
\mathnet{http://mi.mathnet.ru/al112}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2170688}
\zmath{https://zbmath.org/?q=an:1150.17009}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 3
\pages 148--167
\crossref{https://doi.org/10.1007/s10469-005-0017-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-22444433900}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Remeslennikov V., Stöhr R., “The equation $[x,u]+[y,v]=0$ in free Lie algebras”, Internat. J. Algebra Comput., 17:5-6 (2007), 1165–1187  crossref  mathscinet  zmath  isi  elib
    2. Daniyarova E., Myasnikov A., Remeslennikov V., “Unification theorems in algebraic geometry”, Aspects of Infinite Groups, Algebra and Discrete Mathematics, 1, 2008, 80–111  mathscinet  zmath  isi
    3. É Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. IV. Equational domains and codomains”, Algebra and Logic, 49:6 (2010), 483–508  mathnet  crossref  mathscinet  isi
    4. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. II. Foundations”, J. Math. Sci., 185:3 (2012), 389–416  mathnet  crossref
    5. A. G. Pinus, “The algebraic and logical geometries of universal algebras (a unified approach)”, J. Math. Sci., 185:3 (2012), 473–483  mathnet  crossref
    6. Altassan A., Stoehr R., “On linear equations in free Lie algebras”, J Algebra, 349:1 (2012), 329–341  crossref  mathscinet  zmath  isi  elib  scopus
    7. Mohammad Shahryari, “Equationally noetherian algebras and chain conditions”, Zhurn. SFU. Ser. Matem. i fiz., 6:4 (2013), 521–526  mathnet
    8. P. Modabberi, M. Shahryari, “Equational conditions in universal algebraic geometry”, Algebra and Logic, 55:2 (2016), 146–172  mathnet  crossref  crossref  isi
    9. P. Modabberi, M. Shahryari, “On the equational Artinian algebras”, Sib. elektron. matem. izv., 13 (2016), 875–881  mathnet  crossref
    10. Khodabandeh H. Shahryari M., “Equations in Polyadic Groups”, Commun. Algebr., 45:3 (2017), 1227–1238  crossref  mathscinet  zmath  isi  scopus
    11. Daniyarova Evelina Yur'evna, Myasnikov A.G., Remeslennikov V.N., “Algebraic Geometry Over Algebraic Structures X: Ordinal Dimension”, Int. J. Algebr. Comput., 28:8, SI (2018), 1425–1448  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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