A combinatorial principle and endomorphism rings. I: On \(p\)-groups

DOI10.1007/BF02760650zbMath0559.20039MaRDI QIDQ2266127

Saharon Shelah

Publication date: 1984

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

large cardinalsindecomposable modulesdirect sumBlack Box\(p\)-adic completionabelian \(p\)-groupsKaplansky's test problemssmall endomorphismsadditive group of rings of \(p\)-adic integersrealized as endomorphism ringtree-methods

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Large cardinals (03E55) Other combinatorial set theory (03E05) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Torsion groups, primary groups and generalized primary groups (20K10)

Related Items (15)

Automorphism groups of fields ⋮ Very decomposable Abelian groups ⋮ Prescribing endomorphism algebras. The cotorsion-free case ⋮ Co-Hopfian and boundedly endo-rigid mixed abelian groups ⋮ The affinity of set theory and abelian group theory. ⋮ Remarks about the history of Abelian groups in England and Germany. ⋮ Notes on monadic logic. Part B: Complexity of linear orders in ZFC ⋮ Quite free complicated abelian groups, pcf and black boxes ⋮ Separable Abelian \(p\)-groups having certain prescribed chains ⋮ Kaplansky test problem for \(R\)-modules ⋮ Abelian groups ⋮ A combinatorial principle and endomorphism rings. I: On \(p\)-groups ⋮ Automorphisms of Torsion-Free Nilpotent Groups of Class Two ⋮ \(\mathrm{ZF}+\mathrm{DC}+\mathrm{AX}_4\) ⋮ All Infinite Groups are Galois Groups Over any Field

Cites Work

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• Modules over arbitrary domains
• Constructions of many complicated uncountable structures and Boolean algebras
• Existence of many \(L_{\infty,\lambda}\)-equivalent, non-isomorphic models of T of power \(\lambda\)
• On endomorphism rings of primary Abelian groups
• Classification theory and the number of non-isomorphic models
• A combinatorial principle and endomorphism rings. I: On \(p\)-groups
• Quasi-Direct Decompositions of Torsion-Free Abelian Groups of Infinite Rank.
• Modules over arbitrary domains II
• Prescribing Endomorphism Algebras, a Unified Treatment

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