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Algebraic Geometry over Groups II. Logical Foundations

✍ Scribed by Alexei Myasnikov; Vladimir Remeslennikov

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 302 KB
Volume: 234
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8414

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✦ Synopsis

The object of this paper, which is the second in a series of three, is to lay the logical foundations of the algebraic geometry over groups. Exploiting links between the algebraic geometry over groups and model theory we solve two problems on geometrical equivalence of groups which are due to B. Plotkin.

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The object of this paper, which is the first in a series of three, is to lay the foundations of the theory of ideals and algebraic sets over groups. ᮊ 1999 Aca- demic Press CONTENTS 1. Introduction. 1.1. Some general comments. 1.2. The category of G-groups. 1.3. Notions from commutative algebra. 1.4