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Title: On cut completions of abelian lattice ordered groups (English)
Author: Jakubík, Ján
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 50
Issue: 3
Year: 2000
Pages: 587-602
Summary lang: English
Category: math
Summary: We denote by $F_a$ the class of all abelian lattice ordered groups $H$ such that each disjoint subset of $H$ is finite. In this paper we prove that if $G \in F_a$, then the cut completion of $G$ coincides with the Dedekind completion of $G$. (English)
Keyword: abelian lattice ordered group
Keyword: disjoint subset
Keyword: cut completion
Keyword: Dedekind completion
MSC: 06F15
MSC: 06F20
idZBL: Zbl 1079.06507
idMR: MR1777479
Date available: 2009-09-24T10:36:01Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] R. N. Ball: The structure of the $\alpha $-completion of a lattice ordered group.Houston J. Math. 15 (1989), 481–515. Zbl 0703.06009, MR 1045509
Reference: [2] R. N. Ball: Completions of $\ell $-groups.In: Lattice Ordered Groups, A. M. W. Glass and W. C. Holland (eds.), Kluwer, Dordrecht-Boston-London, 1989, pp. 142–177. MR 1036072
Reference: [3] R. N. Ball: Distinguished extensions of a lattice ordered group.Algebra Universalis 35 (1996), 85–112. Zbl 0842.06012, MR 1360533, 10.1007/BF01190971
Reference: [4] P. Conrad: The structure of lattice-ordered groups with a finite number of disjoint elements.Michigan Math. J. 7 (1960), 171–180. MR 0116059, 10.1307/mmj/1028998387
Reference: [5] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011
Reference: [6] J. Jakubík: Generalized Dedekind completion of a lattice ordered group.Czechoslovak Math. J. 28 (1978), 294–311. MR 0552650


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