Rings whose modules have nice decompositions

DOI10.1007/BF01110928zbMath0218.13012OpenAlexW2911370709MaRDI QIDQ2546540

Robert B. jun. Warfield

Publication date: 1972

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/171701

Mathematics Subject Classification ID

Principal ideal rings (13F10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Theory of modules and ideals in commutative rings (13C99)

Related Items (19)

A test for finite representation type ⋮ On left Köthe rings and a generalization of a Köthe-Cohen-Kaplansky theorem ⋮ Rings whose Right Modules are Direct Sums of Indecomposable Modules ⋮ Commutative rings with no super-decomposable modules ⋮ CF-modules over commutative rings ⋮ Local rings whose modules are almost serial ⋮ Modules of existentially closed algebras ⋮ Almost uniserial rings and modules. ⋮ Commutative Noetherian local rings whose ideals are direct sums of cyclic modules ⋮ Pure-semisimplicity of the category of graded modules over graded artin algebras ⋮ Commutative rings whose proper ideals are serial ⋮ (Sigma-) algebraic compactness of rings ⋮ Prime uniserial modules and rings ⋮ Sur les anneaux principaux ⋮ Noetherian rings whose modules are prime serial ⋮ On duo rings, pure semisimplicity and finite representation type ⋮ A note on the decompositiosi of σ-injective modules ⋮ Commutative rings whose proper ideals are direct sums of uniform modules ⋮ On the Sparsity of Representations of Rings of Pure Global Dimension Zero

Cites Work

• Projective modules
• Direct-sum representations of injective modules
• Rings for which every module is a direct sum of cyclic modules
• The existence of indecomposable abelian groups of arbitrary power
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Decomposability of Finitely Presented Modules
• Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring

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