| Title:
|
Distinguished completion of a direct product of lattice ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
661-671 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group $G$ is a direct product of lattice ordered groups $G_i$ $(i\in I)$, then $E(G)$ is a direct product of the lattice ordered groups $E(G_i)$. From this we obtain a generalization of a result of Ball [3]. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
distinguished completion |
| Keyword:
|
direct product |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1079.06505 |
| idMR:
|
MR1851554 |
| . |
| Date available:
|
2009-09-24T10:46:04Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127676 |
| . |
| Reference:
|
[1] R. N. Ball: The distinguished completion of a lattice ordered group.In: Algebra Carbondale 1980, Lecture Notes Math. 848, Springer Verlag, 1980, pp. 208–217. MR 0613187 |
| 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 Univ. 35 (1996), 85–112. Zbl 0842.06012, MR 1360533, 10.1007/BF01190971 |
| Reference:
|
[4] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[5] J. Jakubík: Generalized Dedekind completion of a lattice ordered group.Czechoslovak Math. J. 28 (1978), 294–311. MR 0552650 |
| Reference:
|
[6] J. Jakubík: Maximal Dedekind completion of an abelian lattice ordered group.Czechoslovak Math. J. 28 (1978), 611–631. MR 0506435 |
| Reference:
|
[7] J. Jakubík: Distinguished extensions of an $MV$-algebra.Czechoslovak Math. J. 49 (1999), 867–876. MR 1746712, 10.1023/A:1022469521480 |
| . |
