Direct sums of quasi-injective modules, injective covers, and natural classes

DOI10.1080/00927879408825000zbMath0802.16007OpenAlexW1982522012MaRDI QIDQ4295975

Yiqiang Zhou, Stanley S. Page

Publication date: 12 December 1994

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

Full work available at URL: https://doi.org/10.1080/00927879408825000

zbMATH Keywords

direct sumscyclic moduleinjective modulesinjective hullsright idealsquasi-injective modulesascending chain\(K\)-injective cover

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items (6)

Lattices of classes of modules ⋮ Module types ⋮ Direct sums of m-injective modules and module classes ⋮ The lattice of natural classes of modules ⋮ On Disjoint Sets of Natural Classes ⋮ Relative chain conditions and module classes

Cites Work

• Injective and flat covers, envelopes and resolvents
• Cyclic modules whose quotients have all complement submodules direct summands
• Torsion-free covers. II
• Modules whose quotients have finite Goldie dimension
• Rings all of whose finitely generated modules are injective
• On direct representations of quasi-injectives and quasi-projectives
• Torston free injective covers
• Rings all of whose torsion quasi-injective modules are injective
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