Lifting modules, extending modules and their applications to QF-rings

DOI10.14492/hokmj/1381757705zbMath0559.16013OpenAlexW2066126680MaRDI QIDQ2266106

Kiyoichi Oshiro

Publication date: 1984

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14492/hokmj/1381757705

zbMATH Keywords

projective modulesinjective moduleslifting modulesright Artinian ringsextending modulesgeneralized uniserial ringsright annihilator idealsco-H-ringsH-rings

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Quasi-Frobenius rings (16L60) Other classes of modules and ideals in associative algebras (16D80) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items (53)

Strongly CS-Rickart and dual strongly CS-Rickart objects in abelian categories ⋮ MODULES WITH SMALL CYCLIC SUBMODULES IN THEIR INJECTIVE HULLS ⋮ Relatively extending modules. ⋮ On simple submodules and C-rings ⋮ C3-Modules ⋮ Rings for which certain modules are \(CS\) ⋮ On continuous rings ⋮ Self-duality of quasi-Harada rings and locally distributive rings. ⋮ \(\Sigma\)-extending modules ⋮ On indecomposable decompositions of \(CS\)-modules. II ⋮ On generalized extending modules. ⋮ The classification of tilting modules over Harada algebras. ⋮ On a class of Harada rings ⋮ CS-Rickart and dual CS-Rickart objects in abelian categories ⋮ Rings characterised by semiprimitive modules ⋮ The opposite of injectivity by proper classes ⋮ SELF-DUALITY OF HARADA RING OF A COMPONENT TYPE ⋮ On infinite direct sums of lifting modules ⋮ On σ-extending modules ⋮ On some classes of Artinian rings ⋮ On serial Noetherian rings ⋮ D-Extending Modules ⋮ H-supplemented Modules and Generalizations of Quasi-discrete Modules ⋮ ON A CLASS OF SEMIPERFECT RINGS ⋮ Lifting Modules Over Right Perfect Rings ⋮ Lifting Property of Direct Sums of Hollow Modules ⋮ Sigma-cotorsion rings. ⋮ WHEN SELF-INJECTIVE RINGS ARE QF: A REPORT ON A PROBLEM ⋮ Relatively Lifting Modules ⋮ Neat-flat Modules ⋮ Some Results on Self-Injective Rings and Σ-CS Rings ⋮ Lifting Modules with Indecomposable Decompositions ⋮ δ-M-Small and δ-Harada Modules ⋮ Σ-Extending Modules, Σ-Lifting Modules, and Proper Classes ⋮ Projective summands of not singular modules ⋮ Skew-injective modules ⋮ Indecomposable decompositions of modules whose direct sums are CS. ⋮ A note on co-Harada rings ⋮ A note on generalizations of quasi-Frobenius rings ⋮ On Direct ProjectiveH-Supplemented Modules ⋮ On the structure of modules defined by subinjectivity ⋮ Self-duality and Harada rings ⋮ Absolutelys-Pure Modules and Neat-Flat Modules ⋮ Some classes of qf-3 rings ⋮ On the relative (quasi-) continuity of modules ⋮ A CHARACTERIZATION OF CO-HARADA RING ⋮ Rings whose modules have maximal or minimal subprojectivity domain ⋮ Projectivity relative to closed (neat) submodules ⋮ Almost self-duality and Harada rings. ⋮ On weak co-\(H\)-sequences in two-sided Harada rings ⋮ On direct sums of extending modules and internal exchange property ⋮ On rings with envelopes and covers regarding to C3, D3 and flat modules ⋮ Some remarks on CS modules and SI rings

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