Dually slender modules and steady rings

DOI10.1515/form.1997.9.61zbMath0866.16003OpenAlexW2031554985WikidataQ57571346 ScholiaQ57571346MaRDI QIDQ4332187

Paul C. Eklof, Jan Trlifaj, Kenneth R. Goodearl

Publication date: 10 July 1997

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/141793

zbMATH Keywords

finitely generated modulesdirect sumsLoewy lengthdually slender right modulesalmost free modulessteady ringsright semiartinian ringsreducing modules

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Module categories in associative algebras (16D90) Free, projective, and flat modules and ideals in associative algebras (16D40) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Artinian rings and modules (associative rings and algebras) (16P20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Applications of logic in associative algebras (16B70)

Related Items (19)

The defect functor of a homomorphism and direct unions ⋮ Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings ⋮ Socle chains of Abelian regular semiartinian rings. ⋮ Small Modules over Abelian Regular Rings ⋮ Modules \(M\) such that \(\mathrm{Ext}_R^1(M,-)\) commutes with direct limits. ⋮ On socle chains of semiartinian rings with primitive factors Artinian ⋮ Steadiness of regular semiartinian rings with primitive factors Artinian. ⋮ Topologically semisimple and topologically perfect topological rings ⋮ Steady ideals and rings ⋮ Perfect monoids with zero and categories of S-acts ⋮ An elementary result on infinite and finite direct sums of modules ⋮ When Products of Self-Small Modules are Self-Small ⋮ Modules over discrete valuation domains. III ⋮ When every self-small module is finitely generated. ⋮ Mod-Retractable Rings ⋮ Modules Commuting (Via Hom) with Some Colimits ⋮ Compactness in abelian categories ⋮ Autocompact objects of Ab5 categories ⋮ Connected objects in categories of S-acts

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