This article is cited in 35 papers

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

É 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 Science, Omsk, Russia
^b Schaefer School of Engineering and Science, Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, USA

Abstract: 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.

Keywords: algebra, algebraic set, universal algebraic geometry, disjunctive equation, equational domain, equational codomain, discriminating algebra, codiscriminating algebra.

UDC: 512.71+512.577+512.55

Received: 07.08.2010
Revised: 28.11.2010

 English version: Algebra and Logic, 2010, 49:6, 483–508

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