Irreducible algebraic sets over divisible decomposed rigid groups.

DOI10.1007/s10469-009-9071-zzbMath1245.20054OpenAlexW2005974548MaRDI QIDQ431718

N. S. Romanovskii

Publication date: 29 June 2012

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-009-9071-z

zbMATH Keywords

rigid groupssystems of equationsirreducible algebraic setsalgebraic geometry over groupstorsion-free right modulesequationally Noetherian groupsuniversally equivalent groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Derived series, central series, and generalizations for groups (20F14) Algebraic geometry over groups; equations over groups (20F70)

Related Items (21)

Generalized rigid groups: definitions, basic properties, and problems ⋮ Decomposition of a group over an abelian normal subgroup ⋮ Partially divisible completions of rigid metabelian pro-\(p\)-groups ⋮ Algebraic sets in a finitely generated 2-step solvable rigid pro-\(p\)-group. ⋮ Model-theoretic aspects of the theory of divisible rigid soluble groups ⋮ \(\mathbb Q\)-completions of free solvable groups. ⋮ Divisible rigid groups. Morley rank ⋮ Equational Noethericity of metabelian \(r\)-groups ⋮ Generic types and generic elements in divisible rigid groups ⋮ Algebraic geometry over algebraic structures. VI: Geometrical equivalence ⋮ Divisible rigid groups. Algebraic closedness and elementary theory ⋮ Irreducibility of an affine space in algebraic geometry over a group. ⋮ Characterization of finitely generated groups by types ⋮ Divisible rigid groups. IV: Definable subgroups ⋮ Solvability of equations in classes of solvable groups and Lie algebras ⋮ Coordinate groups of irreducible algebraic sets over divisible metabelian \(r\)-groups ⋮ Generalized rigid metabelian groups ⋮ Algebraic sets in a divisible 2-rigid group ⋮ Rigid metabelian pro-\(p\)-groups. ⋮ Automorphisms of divisible rigid groups. ⋮ Logical aspects of the theory of divisible rigid groups.

Cites Work

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• Krull dimension of solvable groups.
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Algebraic geometry over groups. II: Logical foundations
• Applications of a New K-Theoretic Theorem to Soluble Group Rings
• Irreducible Algebraic Sets in Metabelian Groups
• The property of being equationally Noetherian for some soluble groups
• Algebraic sets in metabelian groups
• On algebraic sets over metabelian groups
• A Note on Zero Divisors in Group-Rings

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