A topology on arithmetical lattice-ordered groups
type: Item
instance of: scholarly article
title: A topology on arithmetical lattice-ordered groups
zbMATH Open document ID: 0596.06016
author: Kentaro Murata
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: A lattice ordered group G is called arithmetical, if it is a conditionally complete lattice and the free group generated by the set P of all prime elements in the cone (integral part) of G. There is described the weakest topology on an arithmetical lattice-ordered group for which a given lattice-ideal is open and presented some corollaries, of proved theorems, for some of ring topologies, field topologies and p- adic topologies.
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 54H13
zbMATH DE Number: 3959507
zbMATH Keywords: conditionally complete lattice
zbMATH Keywords: prime elements
zbMATH Keywords: arithmetical lattice- ordered group
zbMATH Keywords: ring topologies
zbMATH Keywords: field topologies
zbMATH Keywords: p-adic topologies
reviewed by: J. Chvalina
MaRDI profile type: Publication
full work available at URL: pjaa.62.101
OpenAlex ID: W1979267248
cites work: Q5509706
cites work: Q5840137
cites work: Q5817480
cites work: On lattice ideals in a conditionally complete lattice-ordered semigroup
cites work: Q3259734
DOI: 10.3792/PJAA.62.101
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description: scientific article; zbMATH DE number 3959507