| 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:
|
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 |
| . |
