Transversally bounded lattices
type: Item
instance of: scholarly article
title: Transversally bounded lattices
zbMATH Open document ID: 0658.06002
DOI: 10.1007/BF00337623
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: The author deals with a problem stemming from a boundedness question for torsion modules and its translation into ideal lattices. The results are part of a round trip from torsion modules to ultrafilters through lattices. The starting point was a problem on torsion modules over commutative integral domains. It is shown that the lattices which are transversally but not uniformly bounded, corresponded to certain ultrafilters with peculiar boundedness properties similar to those studied by Ramsey. The prototypical candidates of the two types of lattices which one is led to construct from ultrafilters appear to be of interest beyond the original questions.
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 4075134
zbMATH Keywords: boundedness
zbMATH Keywords: torsion modules
zbMATH Keywords: ultrafilters
author: Birge Zimmermann Huisgen
MaRDI profile type: Publication
cites work: Descending chains and the Krull ordinal of commutative Noetherian rings
cites work: Transversals of families in complete lattices, and torsion in product modules
cites work: Infinite joins that are finitely join-irreducible
cites work: Boundedness of direct products of torsion modules
cites work: Direct products of torsion modules
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description: scientific article; zbMATH DE number 4075134