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Algebraic Geometry over Algebraic Structures. VIII. Geometric Equivalences and Special Classes of Algebraic Structures

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This paper belongs to our series of works on algebraic geometry over arbitrary algebraic structures. In this one, there will be investigated seven equivalences (namely: geometric, universal geometric, quasi-equational, universal, elementary, and combinations thereof) in specific classes of algebraic structures (equationally Noetherian, qω-compact, uω-compact, equational domains, equational co-domains, etc.). The main questions are the following: (1) Which equivalences coincide inside a given class K, which do not? (2) With respect to which equivalences a given class K is invariant, with respect to which it is not?

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk, Russia

    E. Yu. Daniyarova & V. N. Remeslennikov

  2. Schaefer School of Engineering and Science, Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, USA

    A. G. Myasnikov

Authors
  1. E. Yu. Daniyarova
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  2. A. G. Myasnikov
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  3. V. N. Remeslennikov
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Corresponding author

Correspondence to E. Yu. Daniyarova.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 4, pp. 75–100, 2019.

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Daniyarova, E.Y., Myasnikov, A.G. & Remeslennikov, V.N. Algebraic Geometry over Algebraic Structures. VIII. Geometric Equivalences and Special Classes of Algebraic Structures. J Math Sci 257, 797–813 (2021). https://doi.org/10.1007/s10958-021-05520-1

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  • DOI: https://doi.org/10.1007/s10958-021-05520-1

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