On modules with finite uniform and Krull dimension

DOI10.1007/BF01189998zbMath0763.16002MaRDI QIDQ1193247

Robert Wisbauer, Dinh Van Huynh, Nguyen Viet Dung

Publication date: 27 September 1992

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

Krull dimensioncyclic modulefinitely generated moduledirect sumright Ore domaindirect summandfinite uniform dimensionfinitely cogenerated modulelocally Artinian\(CS\)-module\(M\)- injective modulecyclic subfactor

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) Homological dimension in associative algebras (16E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Artinian rings and modules (associative rings and algebras) (16P20)

Related Items (14)

A note on continuous rings ⋮ Rings for which certain modules are \(CS\) ⋮ Generalized injectivity and chain conditions ⋮ Rings whose cyclics are D3-modules ⋮ On artinian sc-rings ⋮ Rings characterised by semiprimitive modules ⋮ AN AFFIRMATIVE ANSWER TO A QUESTION ON NOETHERIAN RINGS ⋮ Modules arising from some relative injectives ⋮ A characterization of noetherian rings by cyclic modules ⋮ Self-projective modules with \(\pi\)-injective factor modules ⋮ RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN ⋮ Rings whose finitely generated modules are extending ⋮ Rings whose cyclic modules are lifting and ⊕-supplemented ⋮ Rings whose cyclics are U-modules

Cites Work

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• A characterization of locally Artinian modules
• A characterization of rings with Krull dimension
• On rings with restricted minimum condition
• Cyclic modules whose quotients have all complement submodules direct summands
• Rings all of whose finitely generated modules are injective
• A CHARACTERIZATION OF NOETHERIAN MODULES
• A characterization of artinian rings
• Rings Whose Cyclic Modules are Injective or Projective
• Rings Characterized by their Cyclic Modules
• A criterion to decide if a polynomial map is invertible and to compute the inverse

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