On Whitehead modules

DOI10.1016/0021-8693(91)90321-XzbMath0743.16004OpenAlexW2054573115MaRDI QIDQ1178933

Saharon Shelah, Paul C. Eklof

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1016/0021-8693(91)90321-x

zbMATH Keywords

consistencyforcingtest moduleBaer modulesundecidablenon-projective moduleWhitehead \(R\)- modules

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Free, projective, and flat modules and ideals in associative algebras (16D40) Consistency and independence results (03E35) Model-theoretic forcing (03C25) Applications of logic in associative algebras (16B70)

Related Items (14)

Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings ⋮ On *-modules generating the injectives ⋮ On the cogeneration of cotorsion pairs ⋮ Unnamed Item ⋮ The dual Baer criterion for non-perfect rings ⋮ Enochs' conjecture for small precovering classes of modules ⋮ Set Theory Generated by Abelian Group Theory ⋮ Recent Progress in Module Approximations ⋮ Faith’s problem on $R$-projectivity is undecidable ⋮ An independence result on cotorsion theories over valuation domains ⋮ Test sets for factorization properties of modules ⋮ Harmanci Injectivity of Modules ⋮ Tree modules and limits of the approximation theory ⋮ Covers induced by Ext

Cites Work

• Projective modules
• Categoricity results for \(L_{\infty \kappa}\)-free algebras
• Baer modules over valuation domains
• Polyserial modules over valuation domains
• Whitehead groups may not be free even assuming CH. II
• Proper forcing
• Infinite Abelian groups, Whitehead problem and some constructions
• A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals
• Whitehead groups may be not free, even assuming CH. I
• Note on extensions of Abelian groups by primary groups
• Baer Modules over Domains
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Uniformization principles
• Diamonds, uniformization
• Whitehead Modules over Domains
• Homological Algebra and Set Theory
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