# Article

 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: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/127595 . 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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