Decidable representations

DOI10.1016/0022-4049(95)00097-GzbMath0838.16010OpenAlexW4213088535MaRDI QIDQ1903681

Annalisa Marcja, Carlo Toffalori

Publication date: 24 April 1996

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(95)00097-g

zbMATH Keywords

undecidabilityfinite groupsdecision problemsgroup ringsgenus\(\mathbb{Z} G\)-latticeselementary equivalent latticesfive-subspace problemrepresentation-finite lattices

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Group rings (16S34) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Undecidability and degrees of sets of sentences (03D35) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Basic properties of first-order languages and structures (03C07) Applications of logic in associative algebras (16B70)

Related Items

Unnamed Item, An undecidability theorem for lattices over group rings, Wildness implies undecidability for lattices over group rings, Strongly Minimal Modules Over Group Rings, Vaught's Conjecture and Group Rings, The torsionfree part of the Ziegler spectrum of RG when R is a Dedekind domain and G is a finite group

Cites Work

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• Unsolvability of the universal theory of finite groups
• Model theory of modules
• On four subspaces of a vector space
• The first order properties of products of algebraic systems
• Decidability for Theories of Modules
• On the elementary theory of quadruples of vector spaces
• Four concepts from “geometrical” stability theory in modules
• Decidability for modules over a group ring - II
• Decidability for modules over a group ring