| Title:
|
Lexicographic products of half linearly ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
127-138 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4]. (English) |
| Keyword:
|
half linearly ordered group |
| Keyword:
|
lexicographic product |
| Keyword:
|
isomorphic refinements |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1079.06504 |
| idMR:
|
MR1814638 |
| . |
| Date available:
|
2009-09-24T10:40:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127632 |
| . |
| Reference:
|
[1] L. Fuchs: Partially Ordered Algebraic Systems.Pergamon Press, Oxford-London-New York-Paris, 1963. Zbl 0137.02001, MR 0171864 |
| Reference:
|
[2] M. Giraudet and F. Lucas: Groupes à moitié ordonnés.Fund. Math. 139 (1991), 75–89. MR 1150592, 10.4064/fm-139-2-75-89 |
| Reference:
|
[3] J. Jakubík: The mixed product decompositions of partially ordered groups.Czechoslovak Math. J. 20 (1970), 184–206. MR 0258705 |
| Reference:
|
[4] J. Jakubík: On half lattice ordered groups.Czechoslovak Math. J. 46 (1996), 745–767. MR 1414606 |
| Reference:
|
[5] A. I. Maltsev: On ordered groups.Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473–482. (Russian) MR 0032645 |
| . |
