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Algebraic geometry over algebraic structures. IV. Equational domains and codomains

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We introduce and study equational domains and equational codomains. Informally, an equational domain is an algebra every finite union of algebraic sets over which is an algebraic set; an equational codomain is an algebra every proper finite union of algebraic sets over which is not an algebraic set.

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Authors and Affiliations

  1. Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

    É. Yu. Daniyarova

  2. Schaefer School of Engineering and Science, Department of Mathematical Sciences, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ, 07030–5991, USA

    A. G. Myasnikov

  3. Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

    V. N. Remeslennikov

Authors
  1. É. 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 É. Yu. Daniyarova.

Additional information

Supported by RFBR (project No. 08-01-00067).

Translated from Algebra i Logika, Vol. 49, No. 6, pp. 715-756, November-December, 2010.

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Daniyarova, É.Y., Myasnikov, A.G. & Remeslennikov, V.N. Algebraic geometry over algebraic structures. IV. Equational domains and codomains. Algebra Logic 49, 483–508 (2011). https://doi.org/10.1007/s10469-011-9112-2

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  • DOI: https://doi.org/10.1007/s10469-011-9112-2

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