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

Abstract

A general theory of algebraic geometry over an arbitrary algebraic structure A in a language L with no predicates is consistently presented in a series of papers on universal algebraic geometry [5–8]. 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 L.