Stable structure of noncommutative Noetherian rings. II

DOI10.1016/0021-8693(78)90270-3zbMath0391.16010OpenAlexW2027699063MaRDI QIDQ1251265

J. Toby Stafford

Publication date: 1978

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

Full work available at URL: https://doi.org/10.1016/0021-8693(78)90270-3

zbMATH Keywords

Cancellation TheoremNoncommutative Noetherian RingsSerre's TheoremStable Range TheoremFree Direct SummandFree Rank of a ModuleLeft Ideal InvarianceLeft Noetherian Left Weakly Ideal Invariant RingRegular Rank of a ModuleSimple Noetherian RingTorsionfree Rank

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Prime and semiprime associative rings (16N60) 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) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (16)

Modules over the 4-dimensional Sklyanin algebra ⋮ A Simple Noetherian Ring Not Morita Equivalent to a Domain ⋮ The influence of ideal structure on representation theory ⋮ Morita Equivalence of Simple Noetherian Rings ⋮ A note on the module structure of weyl algebras and simple noetherian rings ⋮ Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings ⋮ Basic element theory of noncommutative Noetherian rings ⋮ Dimension de gelfand-kirillov et decomposition primaire bilatere dans certaines algebres filtrees ⋮ A constructive study of the module structure of rings of partial differential operators. ⋮ Ideal invariance and Artinian quotient rings ⋮ The basic element theorem for fully bounded rings and some applications ⋮ Middle annihilators in noetherian rings ⋮ Integral non-commutative spaces. ⋮ Ideal invariance and localization ⋮ Non-holonomic modules over Weyl algebras and enveloping algebras ⋮ Krull dimension of generalized Weyl algebras with noncommutative coefficients

Cites Work

• Stable structure of noncommutative Noetherian rings
• Jacobson's conjecture and modules over fully bounded Noetherian rings
• Generating modules efficiently: Theorems from algebraic K-theory
• \(K\)-theory and stable algebra
• Completely Faithful Modules and Ideals of Simple Noetherian Rings
• Noetherian Rings with Krull Dimension One
• Krull dimension
• Algebraic \(K\)-theory

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