The Krull–Gabriel Dimension of a Serial Ring

DOI10.1081/AGB-120024862zbMath1047.16012MaRDI QIDQ4435166

Gena Puninski

Publication date: 26 November 2003

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

zbMATH Keywords

Krull dimensionlattices of idealsserial ringsKrull-Gabriel dimensionZiegler spectraCantor-Bendixson rankstheories of modulesisolation property

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Noncommutative local and semilocal rings, perfect rings (16L30) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Applications of logic in associative algebras (16B70)

Related Items

Krull-Gabriel dimension of 1-domestic string algebras. ⋮ Ziegler spectra of serial rings ⋮ DECIDABILITY OF THE THEORY OF MODULES OVER PRÜFER DOMAINS WITH INFINITE RESIDUE FIELDS ⋮ Krull–Gabriel dimension and the Ziegler spectrum ⋮ SUPERDECOMPOSABLE PURE INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS ⋮ Decidability of the theory of modules over Prüfer domains with dense value groups

Cites Work

• Model theory of modules
• The Krull-Gabriel dimension of the representation theory of a tame hereditary Artin algebra and applications to the structure of exact sequences
• The endomorphism ring of a localized coherent functor
• Co-existence of Krull filtrations
• On the Krull-Gabriel dimension of an algebra
• Ziegler spectra of serial rings with krull dimension
• Generic Modules Over Artin Algebras
• Cantor-Bendixson Rank of the Ziegler Spectrum Over a Commutative Valuation Domain
• Some model theory over a nearly simple uniserial domain and decompositions of serial modules