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Algebra Logika, 2012, Volume 51, Number 1, Pages 41–60 (Mi al521)  

This article is cited in 14 scientific papers (total in 14 papers)

Algebraic geometry over algebraic structures. V. The case of arbitrary signature

E. Yu. Daniyarovaa, A. G. Myasnikovb, V. N. Remeslennikova

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk, Russia
b Schaefer School of Engineering and Science, Dep. of Math. Sci., Stevens Institute of Technology, Hoboken, NJ, USA

Abstract: A general theory of algebraic geometry over an arbitrary algebraic structure $\mathcal A$ in a language $\mathrm L$ with no predicates is consistently presented in a series of papers on universal algebraic geometry [B. Fine (ed.) et al., Aspects of infinite groups. A Festschrift in honor of A. Gaglione (Papers of the conf., Fairfield, USA, March 2007 in honour of A. Gaglione's 60th birthday), (Algebra Discr. Math. (Hackensack), 1), Hackensack, NJ, World Sci., 2008, 80–111; submitted to Fund. Appl. Math.; Southeast Asian Bull. Math., accepted for publ.; Algebra i Logika, 49, No. 6 (2010), 715–756]. The restriction that we impose on the language is not crucial. This is done for the sake of readers who only get acquainted with universal algebraic geometry. Here we show how the entire material accumulated in works on universal geometry can be carried over without essential changes to the case of an arbitrary signature $\mathrm L$.

Keywords: universal algebraic geometry, algebraic structure, algebraic set, coordinate algebra.

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English version:
Algebra and Logic, 2012, 51:1, 28–40

Bibliographic databases:

UDC: 510.67+512.71
Received: 23.05.2011

Citation: E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. V. The case of arbitrary signature”, Algebra Logika, 51:1 (2012), 41–60; Algebra and Logic, 51:1 (2012), 28–40

Citation in format AMSBIB
\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Algebraic geometry over algebraic structures.~V. The case of arbitrary signature
\jour Algebra Logika
\yr 2012
\vol 51
\issue 1
\pages 41--60
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 1
\pages 28--40

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    1. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Dimension in universal algebraic geometry”, Dokl. Math., 90:1 (2014), 450–452  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. N. Shevlyakov, “Universal algebraic geometry with relation $\not=$”, Algebra and Logic, 55:4 (2016), 330–339  mathnet  crossref  crossref  isi
    3. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VI. Geometric equivalence”, Algebra and Logic, 56:4 (2017), 281–294  mathnet  crossref  crossref  isi
    4. A. Tsurkov, “Automorphic equivalence in the classical varieties of linear algebras”, Int. J. Algebr. Comput., 27:8 (2017), 973–999  crossref  mathscinet  zmath  isi  scopus
    5. A. G. Pinus, “Algebraic sets of universal algebras and algebraic closure operator”, Lobachevskii J. Math., 38:4, SI (2017), 719–723  crossref  mathscinet  zmath  isi  scopus
    6. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Universal geometrical equivalence of the algebraic structures of common signature”, Siberian Math. J., 58:5 (2017), 801–812  mathnet  crossref  crossref  isi  elib  elib
    7. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits”, Algebra and Logic, 57:6 (2019), 414–428  mathnet  crossref  crossref  isi
    8. 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
    9. Nikitin A.Yu., Kudyk I.D., Mechanical Science and Technology Update (Mstu-2018), Journal of Physics Conference Series, 1050, IOP Publishing Ltd, 2018  crossref  isi  scopus
    10. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad algebraicheskimi sistemami. VIII. Geometricheskie ekvivalentnosti i osobye klassy algebraicheskikh sistem”, Fundament. i prikl. matem., 22:4 (2019), 75–100  mathnet
    11. Wu J., Zhang J., “Introducing Geometric Signatures of Architecture, Engineering, and Construction Objects and a New Bim Dataset”, Computing in Civil Engineering 2019: Visualization, Information Modeling, and Simulation, eds. Cho Y., Leite F., Behzadan A., Wang C., Amer Soc Civil Engineers, 2019, 264–271  isi
    12. Nikitin A.Yu., Xii International Scientific and Technical Conference Applied Mechanics and Systems Dynamics, Journal of Physics Conference Series, 1210, IOP Publishing Ltd, 2019  crossref  isi  scopus
    13. Tsurkov A., “Automorphic Equivalence in the Varieties of Representations of Lie Algebras”, Commun. Algebr., 48:1 (2020), 397–409  crossref  mathscinet  zmath  isi  scopus
    14. J. Simões da Silva, A. Tsurkov, “Geometrical equivalence and action type geometrical equivalence of group representations”, Algebra Discrete Math., 30:2 (2020), 273–281  mathnet  crossref
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