On consequences of stability

DOI10.1080/00927878108822616zbMath0463.16004OpenAlexW2081632870MaRDI QIDQ3913543

Zoltan Papp, Robert F. Damiano

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1080/00927878108822616

zbMATH Keywords

Krull dimensioninjective envelopeinjective dimensionsstable categoriesuniform dimensionlocalizing subcategoriesfully left bounded ringscommutative noetherian ringsleft stable ringstable regular ringsstable valuation rings

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Commutative Noetherian rings and modules (13E05) Valuation rings (13F30) Commutative rings and modules of finite generation or presentation; number of generators (13E15) 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)

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Stability of abelian groups in a topos of sheaves ⋮ Structure of projectively stable Artinian rings ⋮ On the idempotence and stability of kernel functors ⋮ The Global Dimension of FBN Rings with enough Clans ⋮ Twisted polynomial rings satisfying a polynomial identity ⋮ Minimal injective resolutions and Bass invariants of modules over left stable left Noetherian rings ⋮ Commutative torsion stable rings ⋮ Critical series over stable noetherian rings with applications to prime principal right ideal rings ⋮ Stable torsion radicals over Noetherian rings

Cites Work

• Finiteness of the injective hull
• Théorie primaire de la décomposition dans les anneaux semi-noetheriens
• The Dual of the Notion of “Finitely Generated”
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