Direct sums of m-injective modules and module classes

DOI10.1080/00927879508825258zbMath0824.16006OpenAlexW1988126497MaRDI QIDQ4327991

Yiqiang Zhou

Publication date: 1 November 1995

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

Full work available at URL: https://doi.org/10.1080/00927879508825258

zbMATH Keywords

direct sumsascending chain conditionquasi-injective modulesuniform moduleslocally Noetherian modulescocritical modules\(M\)-injective hulls\(M\)-natural classACC on right \(\tau\)-dense idealsstable hereditary torsion theorysubmodules of \(M\)- generated modules

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) 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 (13)

Lattices of classes of modules ⋮ Module types ⋮ On derived groups of division rings II ⋮ The lattice of natural classes of modules ⋮ Modules arising from some relative injectives ⋮ Weak injectivity and module classes ⋮ RELATIVE INJECTIVITY OF MODULES AND EXCELLENT EXTENSIONS ⋮ Ideals, Natural Classes, and Functors ⋮ On Disjoint Sets of Natural Classes ⋮ NATURAL CLASSES AND TORSION THEORIES ⋮ Relative chain conditions and module classes ⋮ On some classes ofR-modules and congruences inR-tors ⋮ Relative continuity of direct sums of M-injective modules

Cites Work

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• Cyclic modules whose quotients have all complement submodules direct summands
• Rings which have flat injective modules
• Classes of Modules
• Localization of modules and the central closure of rings
• Injectives containihg no proper quasi-injective submodules
• An Unusual Ring
• Direct sums of quasi-injective modules, injective covers, and natural classes
• On Direct Sums of Injective Modules and Chain Conditions

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