Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings

DOI10.1016/0021-8693(81)90208-8zbMath0456.16026OpenAlexW2150797899MaRDI QIDQ1150430

J. Toby Stafford

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)90208-8

zbMATH Keywords

Krull dimensionfinitely generated moduleminimal number of generatorscancellation theoremSerre's theoremForster-Swan theoremGoldie's theoremstable range theorems

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Grothendieck groups, (K)-theory, etc. (16E20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Representation theory of associative rings and algebras (16Gxx)

Related Items (19)

Cancellation of finite-dimensional Noetherian modules ⋮ A nonembeddable Noetherian ring ⋮ Absolute stable rank and quadratic forms over noncommutative rings ⋮ Non-commutative regular local rings of dimension 2 ⋮ Locally free (ℙⁿ)-modules ⋮ Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings ⋮ State spaces of \(K_ 0\) of Noetherian rings ⋮ On primitive ideals in group rings ⋮ On the Ideals of a Noetherian Ring ⋮ Basic element theory of noncommutative Noetherian rings ⋮ The basic element theorem for fully bounded rings and some applications ⋮ Embedding Noetherian rings in Artinian rings ⋮ Epimorphisms between the free groups in a variety of groups ⋮ Generating Modules Efficiently Over Noncommutative Noetherian Rings ⋮ Presentations over HNP rings with enough invertible ideals and torsionfree cancellation over neoclassical orders ⋮ Homological properties of the enveloping algebra U(Sl₂) ⋮ Differential operator rings whose prime factors have bounded Goldie dimension ⋮ Generalizing Serre’s Splitting Theorem and Bass’s Cancellation Theorem via free-basic elements ⋮ State spaces, finite algebras, and skew group rings

Cites Work

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• Stable structure of noncommutative Noetherian rings. II
• Generating modules efficiently: Theorems from algebraic K-theory
• Über die Anzahl der Erzeugenden eines Ideals in einem Noetherschen Ring
• The number of generators of a module
• \(K\)-theory and stable algebra
• On the Stable Range of Right Noetherian Rings
• K -Theory and Stable Structure of Some Noetherian Group Rings
• Stable equivalence of matrices and resolutions
• Krull dimension
• Algebraic \(K\)-theory
• Ideal invariance and Artinian quotient rings

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