Ideals, Natural Classes, and Functors

DOI10.1080/00927871003757535zbMath1221.16008OpenAlexW2059580006MaRDI QIDQ3579899

John Dauns

Publication date: 11 August 2010

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

Full work available at URL: https://doi.org/10.1080/00927871003757535

zbMATH Keywords

lattices of idealsmodule categoriesBoolean latticescomplement submodulesnatural classescomplement closures of submodulesrational extensions of modulessecond singular submodules

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Ideals in associative algebras (16D25)

Cites Work

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• Torsion free modules
• Decomposing modules into direct sums of submodules with types
• The lattice of pre-natural classes of modules
• Module types
• Sublattices of the lattice of pre-natural classes of modules
• Type submodules and direct sum decompositions of modules.
• Relative chain conditions and module classes
• Lattices of classes of modules
• On Direct Sums of Injective Modules and Chain Conditions
• Direct sums of m-injective modules and module classes
• NATURAL CLASSES AND TORSION THEORIES

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