Generating Modules Efficiently Over Noncommutative Noetherian Rings

DOI10.2307/2001560zbMath0719.16014OpenAlexW4251054194MaRDI QIDQ5751022

S. C. Coutinho

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2001560

zbMATH Keywords

stabilityupper boundprime idealsprojective moduleKrull dimensionprimitive idealsfinitely generated moduleFBN ringsminimal number of generatorsbasic dimensionCancellation TheoremSerre's Theoremleft and right Noetherian ringlocal number of generatorsGoldie quotient ringweak ideal invariancecritical composition seriesJ-primesFoster-Swan Theorem

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Ideals in associative algebras (16D25) 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) Stability for projective modules (19A13) Efficient generation of modules (19A15)

Related Items

Basic element theory of noncommutative Noetherian rings

Cites Work

• Non-holonomic modules over Weyl algebras and enveloping algebras
• A nonembeddable Noetherian ring
• The number of generators of a module over a fully bounded ring
• Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings
• Basic element theory of noncommutative Noetherian rings
• Jacobson's conjecture and modules over fully bounded Noetherian rings
• Generating modules efficiently: Theorems from algebraic K-theory
• Krull dimension
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