Decidability of the theory of modules over commutative valuation domains

DOI10.1016/j.apal.2006.09.002zbMath1111.03011OpenAlexW2098833406MaRDI QIDQ866569

V. Puninskaya, Gena Puninski, Carlo Toffalori

Publication date: 14 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.apal.2006.09.002

zbMATH Keywords

decidabilityZiegler spectrumcommutative valuation domaintheory of modules

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Decidability of theories and sets of sentences (03B25) Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Theory of modules and ideals in commutative rings (13C99)

Related Items

THE ZIEGLER SPECTRUM OF THE RING OF ENTIRE COMPLEX VALUED FUNCTIONS ⋮ Some model theory of modules over Bézout domains. The width ⋮ DECIDABILITY OF THE THEORY OF MODULES OVER PRÜFER DOMAINS WITH INFINITE RESIDUE FIELDS ⋮ Unnamed Item ⋮ On the decidability of the theory of modules over the ring of algebraic integers ⋮ Bézout domains and lattice-valued modules ⋮ Valued modules on skew polynomial rings and Bézout domains ⋮ Decidability and modules over Bézout domains ⋮ Decidability of the theory of modules over Prüfer domains with dense value groups ⋮ DECIDABILITY FOR THEORIES OF MODULES OVER VALUATION DOMAINS

Cites Work

• Model theory of modules
• Relative injectivity and pure-injective modules over Prüfer rings
• Cantor-Bendixson Rank of the Ziegler Spectrum Over a Commutative Valuation Domain
• The elementary theory of abelian groups
• Elementary properties of Abelian groups
• Unnamed Item
• Unnamed Item