Modules complemented with respect to a torsion theory

DOI10.1080/00927879708825921zbMath0879.16017OpenAlexW2057895520MaRDI QIDQ4338222

Jorge E. Viola-Prioli, Ana M. da Rocha de Viola-Prioli, Patrick F. Smith

Publication date: 22 January 1998

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

Full work available at URL: https://doi.org/10.1080/00927879708825921

zbMATH Keywords

hereditary torsion theoriesdecomposition theoremsGoldie torsion theoryextending moduleschain conditionstorsion functors\(\mu\)-complemented modulesJansian torsion theory

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items (8)

On \(\tau\)-extending modules. ⋮ On μ-complemented and singular modules ⋮ The Osofsky-Smith Theorem for Modular Lattices, and Applications (II) ⋮ DECOMPOSITIONS OF MODULES SUPPLEMENTED RELATIVE TO A TORSION THEORY ⋮ ON THE OSOFSKY–SMITH THEOREM ⋮ On τ-completely decomposable modules ⋮ Extending modules relative to a torsion theory ⋮ The smallest closed subcategory containing the μcomplemented modules

Cites Work

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• Extending modules over commutative domains
• Modules with many direct summands
• Rings whose kernel functors are linearly ordered
• On absolutely torsion-free rings
• A CHARACTERIZATION OF NOETHERIAN MODULES
• Rings with dcc on essential left ideals
• Modules Over Dedekind Rings and Valuation Rings

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