Decomposing modules into direct sums of submodules with types

DOI10.1016/S0022-4049(97)00208-9zbMath0955.16007MaRDI QIDQ1295761

Yiqiang Zhou

Publication date: 27 February 2001

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

direct sumsdirect summandsinjective hullsextending modulesascending chain conditiondecomposition theoryquasi-continuous modulescomplement submodules\(TS\)-modules with \(T_3\)natural classes of modulesorthogonal modulestype right idealstype submodules

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classes of modules and ideals in associative algebras (16D80)

Related Items (9)

p-semisimple modules and type submodules ⋮ Cotype dimension and cotype chain conditions ⋮ On type-ADS modules and rings ⋮ Ideals, Natural Classes, and Functors ⋮ On Disjoint Sets of Natural Classes ⋮ Modules which are invariant under idempotents of their envelopes ⋮ NATURAL CLASSES AND TORSION THEORIES ⋮ Type submodules and direct sum decompositions of modules. ⋮ Sublattices of the lattice of pre-natural classes of modules

Cites Work

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• Extending modules over commutative domains
• Module types
• On injective and quasi-continuous modules
• Direct sum properties of quasi-injective modules
• Dimension theory for nonsingular injective modules
• RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
• On Direct Sums of Injective Modules and Chain Conditions
• The lattice of natural classes of modules

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