Model theory of modules over a serial ring

DOI10.1016/0168-0072(94)00017-WzbMath0822.03019MaRDI QIDQ1842127

Ivo Herzog, Paul C. Eklof

Publication date: 28 September 1995

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

zbMATH Keywords

uniserial moduleslocal ringvaluation ringarithmetical ringserial ringindecomposable pure-injective modulespositive-primitive formulaspure injective hull

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Structure, classification theorems for modules and ideals in commutative rings (13C05) Applications of logic to commutative algebra (13L05) Applications of logic in associative algebras (16B70)

Related Items

Ziegler spectra of serial rings with krull dimension, Unnamed Item, Vapnik-Chervonenkis density in some theories without the independence property. II, Sobriety for the Ziegler spectrum of a Prüfer domain, Notes on model theory of modules over Dedekind domains, Ziegler spectra of serial rings, Endomorphism rings, power series rings, and serial modules, Unnamed Item, Unnamed Item, DECIDABILITY OF THE THEORY OF MODULES OVER PRÜFER DOMAINS WITH INFINITE RESIDUE FIELDS, Some model theory over a nearly simple uniserial domain and decompositions of serial modules, Vaught's conjecture for modules over a serial ring, Semidistributive modules, Some model theory over hereditary Noetherian domains, Decidability of the theory of modules over Prüfer domains with dense value groups

Cites Work

• Model theory of modules
• Relative injectivity and pure-injective modules over Prüfer rings
• Serial rings and finitely presented modules
• Algebraically compact rings and modules
• Purity and algebraic compactness for modules
• Modules with decompositions that complement direct summands
• Kaplansky's Problem on Valuation Rings
• Four concepts from “geometrical” stability theory in modules
• Modules Whose Lattice of Submodules is Distributive
• Rein injektive direkte summen von moduln
• Arithmetical rings
• Decomposability of Finitely Presented Modules
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