The Kaplansky test problems -- An approach via radicals

DOI10.1016/0022-4049(93)E0182-4zbMath0847.20051MaRDI QIDQ1906930

Rüdiger Göbel, Brendan Goldsmith

Publication date: 18 February 1996

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

zbMATH Keywords

endomorphism algebrasdiamond principleKaplansky's test problemsstrongly \(\aleph_ 1\)-free Abelian groupsstrongly \(\lambda\)-free Abelian groups

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Consistency and independence results (03E35) Torsion-free groups, infinite rank (20K20) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Cites Work

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• On radicals and products
• A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals
• Independence in Completions and Endomorphism Algebras
• On the Existence of κ-Free Abelian Groups
• -Separable Groups and Kaplansky’s Test Problems
• New Criteria for Freeness in Abelian Groups. II
• When Does Almost Free Imply Free? (For Groups, Transversals, etc.)
• Every Cotorsion-Free Ring is an Endomorphism Ring
• χ_n-FREE ABELIAN GROUPS
• Prescribing Endomorphism Algebras, a Unified Treatment
• ON ENDOMORPHISM RINGS OF PRIMARY ABELIAN GROUPS
• Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring

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