Lengths of submodule chains versus Krull dimension in non-Noetherian modules

DOI10.1007/BF01162341zbMath0563.16015OpenAlexW2000542661MaRDI QIDQ1057354

Kenneth R. Goodearl, Birge Zimmermann Huisgen

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173695

zbMATH Keywords

Krull dimensionordinal lengths of well-ordered descending chains of submodules

Mathematics Subject Classification ID

Other classes of modules and ideals in associative algebras (16D80) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Ordinal and cardinal numbers (03E10)

Related Items

On the Countability of Noetherian Dimension of Modules ⋮ Modules with chain condition on uncountably generated submoduled ⋮ Generalized deviations of posets ⋮ Subdirect products of injectives ⋮ GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY ⋮ Dual Krull dimension and quotient finite dimensionality ⋮ The deviation, density, and depth of partially ordered sets ⋮ THE CLOSED-POINT ZARISKI TOPOLOGY FOR IRREDUCIBLE REPRESENTATIONS ⋮ Boundedness of direct products of torsion modules ⋮ THE LENGTH OF NOETHERIAN MODULES

Cites Work

• Unnamed Item
• A theory of length for Noetherian modules
• Boundedness of direct products of torsion modules
• The Gabriel dimension of a module
• Descending chains of submodules and the Krull-dimension of noetherian modules
• Descending chains and the Krull ordinal of commutative Noetherian rings
• The submodule lattice of a cyclic module
• Artinian and nobthekian modules over regular rings
• Krull dimension