Finite splitness and finite projectivity

DOI10.1016/0021-8693(87)90024-XzbMath0607.16017OpenAlexW2058257284WikidataQ105666703 ScholiaQ105666703MaRDI QIDQ1085253

Goro Azumaya

Publication date: 1987

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90024-x

zbMATH Keywords

projective modulesflat modulespure-injective modulesBass submodules of free modulespurity of epimorphismspurity of submodulessplitting epimorphisms

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Automorphisms and endomorphisms (16W20)

Related Items (39)

Precover completing domains and approximations ⋮ Flat modules over valuation rings ⋮ Relatively extending modules. ⋮ Rings in which certain right ideals are direct summands of annihilators ⋮ Rickart and dual Rickart objects in abelian categories: transfer via functors ⋮ Rings satisfying every finitely generated module has a Gorenstein projective (pre)envelope ⋮ When every flat ideal is finitely projective ⋮ Decomposition properties of strict Mittag-Leffler modules. ⋮ Injective and coherent endomorphism rings relative to some matrices ⋮ Injective modules and fp-injective modules over valuation rings. ⋮ On projectivity of finitely generated modules ⋮ Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories ⋮ On envelopes with the unique mapping property ⋮ Strongly Rickart objects in abelian categories ⋮ A note on existence of envelopes and covers ⋮ $\mathcal{F}_{\mathcal{S}}$-MITTAG-LEFFLER MODULES AND GLOBAL DIMENSION RELATIVE TO $\mathcal{F}_{\mathcal{S}}$-MITTAG-LEFFLER MODULES ⋮ Finitely projective modules with respect to a semidualizing module ⋮ Properties of Modules and Rings Relative to Some Matrices ⋮ On rings over which every flat left module is finitely projective ⋮ Accessible subcategories of modules and pathological objects ⋮ Relatively divisible and relatively flat objects in exact categories ⋮ n-INJECTIVE ANDn-FLAT MODULES ⋮ One dimensional tilting modules are of finite type. ⋮ New characterizations of pseudo-coherent rings ⋮ Minimal pure epimorphisms ⋮ A solution to the Baer splitting problem ⋮ Various Classes of Pseudoprojective Modules over Semiperfect Rings ⋮ Σ-Extending Modules, Σ-Lifting Modules, and Proper Classes ⋮ Relatively divisible and relatively flat objects in exact categories: applications ⋮ On General Injective Rings with Chain Conditions ⋮ Relative Projective Modules and Relative Injective Modules ⋮ Relative Flatness, Mittag–Leffler Modules, and Endocoherence ⋮ Cotorsion modules and relative pure-injectivity ⋮ When every finitely projective ideal is projective ⋮ \(\mathcal{F}\)-copartial morphisms ⋮ On a characterization of perfect rings^* ⋮ On general principally injective rings ⋮ Relative coherence and preenvelopes ⋮ Σ-semi-compact rings and modules

Cites Work

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• On the free product of associative rings
• Pure submodules of direct products of free modules
• Purity and algebraic compactness for modules
• Pure theories
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• Modules with decompositions that complement direct summands
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Universally Torsionless and Trace Modules
• Absolutely Pure Modules
• On finitely injective modules

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