Near-discreteness of modules and spaces as measured by Gabriel and Cantor

DOI10.1016/0022-4049(89)90141-2zbMath0663.06007OpenAlexW2058487089MaRDI QIDQ1114723

Harold Simmons

Publication date: 1989

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(89)90141-2

zbMATH Keywords

derivativelattice of submodulesidiomGabriel dimensionCantor-Bendixson analysislattice of congruence relationsGabriel rankmodular meet-continuous latticenon- distributive frame

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Complete lattices, completions (06B23) Topological spaces and generalizations (closure spaces, etc.) (54A05) Continuous lattices and posets, applications (06B35) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items

On the De Morgan's laws for modules, Dimension and decomposition in modular upper-continuous lattices, The semiring of topologizing filters of a ring, The frame of nuclei on an Alexandroff space, Boolean perspectives of idioms and the Boyle derivative, Generalized deviations of posets, Some operators and dimensions in modular meet-continuous lattices, On the Atomic Dimension in Module Categories, A decomposition theory for complete modular meet-continuous lattices, An operation related to the Cantor-Bendixson derivative, Higher order dissolutions and Boolean coreflections of locales

Cites Work

• Non-commutative principal ideal rings
• Spatial sublocales and essential primes
• Atomic toposes
• The Gabriel dimension of a module
• Torsion theoretic points and spaces
• The Gabriel Dimension and Cantor-Bendixson Rank of a Ring
• Spaces with Boolean assemblies
• Noetherian simple rings
• Des catégories abéliennes
• Atomless Parts of Spaces.
• Krull dimension
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