Absolute \(E\)-modules

DOI10.1016/j.jpaa.2010.06.027zbMath1217.13003OpenAlexW2022917556MaRDI QIDQ626723

Rüdiger Göbel

Publication date: 18 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2010.06.027

zbMATH Keywords

\(E\)-morphisms\(E\)-ringabsolute \(E\)-modulesabsolute \(E\)-ringsabsolute endomorphism ringabsolute familyabsolute propertyabsolutely rigid family of treescolored treesErdős cardinalsKurepa-Erdős cardinalsUlm subgroup

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Consistency and independence results (03E35) Structure, classification theorems for modules and ideals in commutative rings (13C05) Applications of logic to commutative algebra (13L05) Torsion-free groups, infinite rank (20K20) Other combinatorial set theory (03E05) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Direct sums, direct products, etc. for abelian groups (20K25) Other special types of modules and ideals in commutative rings (13C13)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localizations of abelian Eilenberg-Mac Lane spaces of finite type
• Left rigid rings.
• \(E(R)\)-algebras that are sharply transitive modules.
• Torsion-free nilpotent groups and E-modules
• Modules with absolute endomorphism rings.
• Torsion-free E-modules
• Better quasi-orders for uncountable cardinals
• Large \(E\)-modules exist
• Large E-rings exist
• Cellular spaces, null spaces and homotopy localization
• Absolute graphs with prescribed endomorphism monoid
• Approximations and endomorphism algebras of modules.
• Classifying E-Rings
• An upper cardinal bound on absolute E-rings
• Absolutely indecomposable modules
• Each countable reduced torsion-free commutative ring is a pure subring of an e-ring
• Large superdecomposable E(R)-algebras
• Every Cotorsion-Free Ring is an Endomorphism Ring
• Prescribing Endomorphism Algebras, a Unified Treatment
• The Existence of LargeE(R)-Algebras That Are Sharply Transitive Modules
• A hierarchy of formulas in set theory
• The endomorphism ring of the additive group of a ring
• Constructing sharply transitive R-modules of rank ⩽