On cut completions of abelian lattice ordered groups

Ján Jakubík

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 3, page 587-602
  • ISSN: 0011-4642

Abstract

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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 ∈ F a , then the cut completion of G coincides with the Dedekind completion of G .

How to cite

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Jakubík, Ján. "On cut completions of abelian lattice ordered groups." Czechoslovak Mathematical Journal 50.3 (2000): 587-602. <http://eudml.org/doc/30586>.

@article{Jakubík2000,
abstract = {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 $G$.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {abelian lattice ordered group; disjoint subset; cut completion; Dedekind completion; abelian lattice ordered group; disjoint subset; cut completion; Dedekind completion},
language = {eng},
number = {3},
pages = {587-602},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On cut completions of abelian lattice ordered groups},
url = {http://eudml.org/doc/30586},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Jakubík, Ján
TI - On cut completions of abelian lattice ordered groups
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 587
EP - 602
AB - 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 $G$.
LA - eng
KW - abelian lattice ordered group; disjoint subset; cut completion; Dedekind completion; abelian lattice ordered group; disjoint subset; cut completion; Dedekind completion
UR - http://eudml.org/doc/30586
ER -

References

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  1. The structure of the α -completion of a lattice ordered group, Houston J. Math. 15 (1989), 481–515. (1989) Zbl0703.06009MR1045509
  2. Completions of ℓ -groups, In: Lattice Ordered Groups, A. M. W. Glass and W. C. Holland (eds.), Kluwer, Dordrecht-Boston-London, 1989, pp. 142–177. (1989) MR1036072
  3. 10.1007/BF01190971, Algebra Universalis 35 (1996), 85–112. (1996) Zbl0842.06012MR1360533DOI10.1007/BF01190971
  4. 10.1307/mmj/1028998387, Michigan Math. J. 7 (1960), 171–180. (1960) MR0116059DOI10.1307/mmj/1028998387
  5. Lattice Ordered Groups, Tulane University, 1970. (1970) Zbl0258.06011
  6. Generalized Dedekind completion of a lattice ordered group, Czechoslovak Math. J. 28 (1978), 294–311. (1978) MR0552650

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