The lattice (,⊂) of arbitrary torsion classes for mod-r

DOI10.1080/00927878008822527zbMath0436.16022OpenAlexW2003903297MaRDI QIDQ3876079

Gerhard Herden

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1080/00927878008822527

zbMATH Keywords

hereditary torsion theoriessimple modulesatomscoatomsright semiartinian ringslattice of torsion classes

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) Noncommutative local and semilocal rings, perfect rings (16L30) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Artinian rings and modules (associative rings and algebras) (16P20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (4)

Arbitrary torsion classes and almost free abelian groups ⋮ Pseudocomplements in the lattice of torsion classes ⋮ Arbitrary torsion classes of abelian groups^* ⋮ Simple rings whose lower radicals are atoms

Cites Work

• Unnamed Item
• Torsion theories of simple type
• Decomposition of modules. II: Rings without chain conditions
• A generalization of quasi-Frobenius rings
• Torsionless modules
• Torsion associated with duality
• Some functors arising from the consideration of torsion theories over noncommutative rings
• On Maximal Torsion Radicals

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