Small almost free modules with prescribed topological endomorphism rings.

zbMath1148.20308MaRDI QIDQ2569823

Rüdiger Göbel, A. L. S. Corner

Publication date: 20 October 2005

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/108600

zbMATH Keywords

endomorphismsdirect sums\(\aleph_1\)-free Abelian groupsmodules over commutative ringspathological Abelian groupsrealization of topological rings as endomorphism rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Projective and free modules and ideals in commutative rings (13C10) Continuum hypothesis and Martin's axiom (03E50) Torsion-free groups, infinite rank (20K20) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Topological and ordered rings and modules (16W80) Direct sums, direct products, etc. for abelian groups (20K25)

Related Items (2)

Prescribing endomorphism algebras of \(\aleph_n\)-free modules. ⋮ Absolutely indecomposable modules

Cites Work

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• On endo-rigid, strongly \(\aleph_1\)-free Abelian groups in \(\aleph_1\).
• Every cotorsion-free algebra is an endomorphism algebra
• On uncountable Abelian groups
• Abelian groups without elements of finite order
• Indecomposable Almost Free Modules—The Local Case
• Every Cotorsion-Free Ring is an Endomorphism Ring
• χ_n-FREE ABELIAN GROUPS
• Prescribing Endomorphism Algebras, a Unified Treatment
• Additive categories and a theorem of W. G. Leavitt
• Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring

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