Every Σ-CS-module has an indecomposable decomposition

DOI10.1090/S0002-9939-00-05654-9zbMath0973.16008MaRDI QIDQ2701609

Pedro A. Guil Asensio, José L. Gómez Pardo

Publication date: 19 February 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

indecomposable decompositionsCS-modulesdirect sums of uniform 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)

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Every \(\aleph_1\)-\(\Sigma\)-CS module is \(\Sigma\)-CS., On the number of zeros in the columns of the character table of a group., Continuous modules are clean., CS matrix rings over local rings, A NOTE ON ESSENTIAL EXTENSIONS OF SEMI-SIMPLE MODULES, Rings whose pure-injective right modules are direct sums of lifting modules., ALMOST INJECTIVE MODULES — A BRIEF SURVEY, Sigma-cotorsion rings., Artinian Rings Characterized by Direct Sums of CS Modules, WHEN SELF-INJECTIVE RINGS ARE QF: A REPORT ON A PROBLEM, Rings Whose CS Modules Are Countably Σ-CS, DENSELY CO-HOPFIAN MODULES, Indecomposable decompositions of modules whose direct sums are CS., Generalized Injectivity and Approximations, Two criteria for locally Noetherian Grothendieck categories, The Torsion Theory Cogenerated by δ–M-Small Modules and GCO-Modules, Rings characterized by direct sums of cs modules

Cites Work

• Cyclic modules whose quotients have all complement submodules direct summands
• On indecomposable decompositions of \(CS\)-modules. II
• Modules with indecomposable decompositions that complement maximal direct summands
• \(\Sigma\)-extending modules
• Lifting modules, extending modules and their applications to generalized uniserial rings
• σ-cs-modules
• On σ-extending modules
• On the foundations of inverse monoids and inverse algebras
• Noninjective Cyclic Modules
• Singular torsion and the splitting properties
• On the Decomposition of Nonsingular CS-Modules
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