Algebraic geometry over groups. III: Elements of model theory.

DOI10.1016/J.JALGEBRA.2004.07.038zbMath1078.20025OpenAlexW1974877162MaRDI QIDQ555757

Alexei Kvaschuk, Alexei G. Myasnikov, Vladimir N. Remeslennikov

Publication date: 10 June 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.07.038

zbMATH Keywords

finitely generated groupsvarieties of groupsmodel theoryfree groupsquasivarietiesdefinabilityirreducible componentselementary theoriescoordinate groupsalgebraic geometry over groupsuniversal equivalencesorthogonal systems of domains

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) General structure theorems for groups (20E34) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10)

Related Items (7)

CENTRALISER DIMENSION OF FREE PARTIALLY COMMUTATIVE NILPOTENT GROUPS OF CLASS 2 ⋮ Groups of prime generalized exponent ⋮ Limit groups over coherent right-angled Artin groups ⋮ SOME RESULTS AND PROBLEMS RELATED TO UNIVERSAL ALGEBRAIC GEOMETRY ⋮ ALGEBRAIC LOGIC AND LOGICALLY-GEOMETRIC TYPES IN VARIETIES OF ALGEBRAS ⋮ Isotyped algebras ⋮ First-order aspects of Coxeter groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The verbal topology of a group
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Definable invariants of bilinear mappings
• Algebraic geometry over groups. II: Logical foundations
• The first order properties of products of algebraic systems
• EXPONENTIAL GROUPS 2: EXTENSIONS OF CENTRALIZERS AND TENSOR COMPLETION OF CSA-GROUPS

This page was built for publication: Algebraic geometry over groups. III: Elements of model theory.