Geodesic
Algebraic geometry over algebraic structures. V. The case of arbitrary signature
Algebra i logika, Tome 51 (2012) no. 1, pp. 41-60

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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 set, coordinate algebra.
Mots-clés : algebraic structure 
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E. Yu. Daniyarova; A. G. Myasnikov; V. N. Remeslennikov. Algebraic geometry over algebraic structures. V. The case of arbitrary signature. Algebra i logika, Tome 51 (2012) no. 1, pp. 41-60. http://geodesic.mathdoc.fr/item/AL_2012_51_1_a1/