THE LENGTH OF NOETHERIAN MODULES

DOI10.1081/AGB-120004483zbMath1012.16025MaRDI QIDQ3146310

Gary Brookfield

Publication date: 18 March 2003

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

zbMATH Keywords

Krull dimensionordinal arithmeticNoetherian modulesreduced rankuniform dimensionArtinian modular latticesArtinian partially ordered sets-ordinal valued length functions

Mathematics Subject Classification ID

Modular lattices, Desarguesian lattices (06C05) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Ordinal and cardinal numbers (03E10)

Related Items (7)

A Krull-Schmidt theorem for Noetherian modules ⋮ On the Countability of Noetherian Dimension of Modules ⋮ Unnamed Item ⋮ The Length of Noetherian Polynomial Rings ⋮ The theory of ordinal length ⋮ THE SPACE OF FINITELY GENERATED RINGS ⋮ A note on Euclidean order types

Cites Work

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• The deviation, density, and depth of partially ordered sets
• A theory of length for Noetherian modules
• Lengths of submodule chains versus Krull dimension in non-Noetherian modules
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• The Krull ordinal and length of a Noetherian module
• On the Krull-dimension of left noetherian left Matlis-rings
• Completely Faithful Modules and Ideals of Simple Noetherian Rings
• Transfinite powers of the jacobson radical

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