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Algebraic geometry over algebraic structures. II. Foundations

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In this paper, we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove so-called unification theorems that describe coordinate algebras of algebraic sets in several different ways.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch of the Russian Academy of Science, 644099, Pevtsova 13, Omsk, Russia

    E. Yu. Daniyarova & V. N. Remeslennikov

  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

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  1. E. Yu. Daniyarova
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  2. A. G. Myasnikov
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  3. V. N. Remeslennikov
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Correspondence to E. Yu. Daniyarova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 1, pp. 65–106, 2011/12.

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Daniyarova, E.Y., Myasnikov, A.G. & Remeslennikov, V.N. Algebraic geometry over algebraic structures. II. Foundations. J Math Sci 185, 389–416 (2012). https://doi.org/10.1007/s10958-012-0923-z

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