Algebraic geometry over algebraic structures. II. Foundations

被引：10
作者：
E. Yu. Daniyarova
A. G. Myasnikov
V. N. Remeslennikov
机构：
[1] Institute of Mathematics, Siberian Branch of the Russian Academy of Science, 644099 Omsk
[2] Schaefer School of Engineering and Science, Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030-5991, Castle Point on Hudson
来源：
Journal of Mathematical Sciences | 2012年 / 185卷 / 3期
关键词：
Algebraic Geometry; Metabelian Group; Zariski Topology; Coordinate Algebra; Qvar;
D O I：
10.1007/s10958-012-0923-z
中图分类号：
学科分类号：
摘要：
In this paper, we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove so-called unification theorems that describe coordinate algebras of algebraic sets in several different ways. © 2012 Springer Science+Business Media, Inc.
引用
收藏
页码：389 / 416
页数：27
相关论文
共 78 条
[1]  
Appel K.I., One-variable equations in free groups, Proc. Am. Math. Soc., 19, pp. 912-918, (1968)
[2]  
Barr M., Wells C., Toposes, triples and theories, Theory Appl. Categ., 1, pp. 1-289, (2005)
[3]  
Baumslag G., Myasnikov A., Remeslennikov V., Algebraic geometry over groups. I. Algebraic sets and ideal theory, J. Algebra, 219, pp. 16-79, (1999)
[4]  
Baumslag G., Myasnikov A., Romankov V., Two theorems about equationally Noetherian groups, J. Algebra, 194, pp. 654-664, (1997)
[5]  
Bryant R., The verbal topology of a group, J. Algebra, 48, pp. 340-346, (1977)
[6]  
Casals-Ruiz M., Kazachkov I., Elements of algebraic geometry and the positive theory of partially commutative groups, Can. J. Math., 62, 3, pp. 481-519, (2010)
[7]  
Casals-Ruiz M., Kazachkov I., On Systems of Equations Over Free Partially Commutative
[8]  
Casals-Ruiz M., Kazachkov I., On Systems of Equations Over Free Products of Groups
[9]  
Champetier C., Guirardel V., Limit groups as limits of free groups: Compactifying the set of free groups, Israel J. Math., 146, pp. 1-76, (2005)
[10]  
Chapuis O., ∀-free metabelian groups, J. Symb. Logic, 62, pp. 159-174, (1997)
12345678