Quotient rings and localization for Noetherian rings

DOI10.1016/0021-8693(81)90316-1zbMath0472.16001OpenAlexW2019537639MaRDI QIDQ1158235

Robert B. jun. Warfield

Publication date: 1981

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(81)90316-1

zbMATH Keywords

regular elementsannihilatorsreduced ranklocalizabilityright Krull dimensionminimal primesGoldie's theoremOre setartinian quotient ringcellular seriesright maximal cells

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items

Links between prime ideals in differential operator rings ⋮ Associated series and regular elements of Noetherian rings ⋮ Criteria for a ring to have a left Noetherian left quotient ring ⋮ Additive rank functions in Noetherian rings ⋮ Rings with an additive rank function ⋮ Krull symmetric Noetherian rings and their homogeneous components

Cites Work

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• Artinian quotient rings of ideal invariant Noetherian rings
• Reduced rank in Noetherian rings
• Artinian quotient rings of FBN rings
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• Shorter Notes: Artinian Ideals in Noetherian Rings
• Localization in Non-Commutative Noetherian Rings
• A Decomposition Theorem for Noetherian orders in Artinian Rings
• Ideal invariance and localization
• Des catégories abéliennes
• On two-sided artinian quotient rings
• Localization of Right Noetherian Rings at Semiprime Ideals
• Injective modules and classical localization in Noetherian rings
• Krull dimension
• Ideal invariance and Artinian quotient rings

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