Whitehead test modules

DOI10.1090/S0002-9947-96-01494-8zbMath0865.16006OpenAlexW1531943980MaRDI QIDQ4889970

Jan Trlifaj

Publication date: 7 July 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01494-8

zbMATH Keywords

projective modulesuniformizationsimple modulesright perfect ringsWhitehead problemgeneralized upper triangular matrix ringsfully saturated ringsconsistency with ZFC+GCHgeneralized weak diamond principlei-test modulesp-test modulesWhitehead test modules for injectivityWhitehead test modules for projectivity

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Large cardinals (03E55) Extensions of abelian groups (20K35) Applications of logic in associative algebras (16B70)

Related Items (32)

Unnamed Item ⋮ Perpendicular categories of infinite dimensional partial tilting modules and transfers of tilting torsion classes. ⋮ Closure properties of \(\varinjlim \mathcal{C}\) ⋮ Modules \(M\) such that \(\mathrm{Ext}_R^1(M,-)\) commutes with direct limits. ⋮ Tilting classes over wild hereditary algebras. ⋮ RD-projective module whose subprojectivity domain is minimal ⋮ Rings admitting nonzero homomorphisms between non-injective modules ⋮ The dual Baer criterion for non-perfect rings ⋮ Rings and modules characterized by opposites of injectivity. ⋮ Almost free modules and Mittag-Leffler conditions. ⋮ Rings whose RD-flat modules have restricted subflat domains ⋮ The opposite of injectivity by proper classes ⋮ Subprojectivity domains of pure-projective modules ⋮ Partial cotilting modules and the lattices induced by them ⋮ Subprojectivity in abelian categories ⋮ Cotilting modules and homological ring epimorphisms ⋮ On the existence of a single test module ⋮ On subinjectivity domains of pure-injective modules ⋮ Faith’s problem on $R$-projectivity is undecidable ⋮ When are torsionless modules projective? ⋮ Category of n -weak injective and n -weak flat modules with respect to special super presented modules ⋮ Completeness of cotorsion pairs ⋮ Hereditary cotilting modules ⋮ Test sets for factorization properties of modules ⋮ Approximation Presentations of Modules and Homological Conjectures ⋮ On the structure of modules defined by subinjectivity ⋮ Max-projective modules ⋮ Covers induced by Ext ⋮ Rings whose modules have maximal or minimal subprojectivity domain ⋮ On subinjectivity domains of RD-injective modules ⋮ When \(R\) is a testing module for projectivity? ⋮ Tilting modules over small Dedekind domains

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