On Direct Sums of Injective Modules and Chain Conditions

DOI10.4153/CJM-1994-034-9zbMath0807.16006WikidataQ114021681 ScholiaQ114021681MaRDI QIDQ4301773

Stanley S. Page, Yiqiang Zhou

Publication date: 14 August 1994

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

torsion theoriesdirect sumsascending chain condition\(M\)-injective modulesdirect sum of uniform moduleshereditary torsion class\(M\)-injective hulls\(M\)-natural classunitary right \(R\)-modules

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) 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 (20)

On simple, primitive and prime rings relative to a torsion theory ⋮ Lattices of classes of modules ⋮ Module types ⋮ On topological \(M\)-injective modules ⋮ Direct sums of m-injective modules and module classes ⋮ The lattice of natural classes of modules ⋮ Weak injectivity and module classes ⋮ NOTES ON NILPOTENCY OF NIL SUBRINGS OF ENDOMORPHISM RINGS OF MODULES ⋮ ON THE LATTICES OF NATURAL AND CONATURAL CLASSES INR-MOD ⋮ On τ-completely decomposable modules ⋮ Ideals, Natural Classes, and Functors ⋮ On Disjoint Sets of Natural Classes ⋮ δ-M-Small and δ-Harada Modules ⋮ On L-injective modules ⋮ NATURAL CLASSES AND TORSION THEORIES ⋮ Decomposing modules into direct sums of submodules with types ⋮ Sublattices of the lattice of pre-natural classes of modules ⋮ Relative chain conditions and module classes ⋮ Rings for Which the Lattice of Hereditary Torsion Theories and the Lattice of Natural Classes are Isomorphic ⋮ Relative continuity of direct sums of M-injective modules

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