This article is cited in 25 papers

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

E. Yu. Daniyarova^a, A. G. Myasnikov^b, V. N. Remeslennikov<sup>a

a</sup> 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.

UDC: 510.67+512.71

Received: 23.05.2011

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

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