| Title:
|
On orthogonally $\sigma$-complete lattice ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
881-888 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove a theorem of Cantor-Bernstein type for orthogonally $\sigma $-complete lattice ordered groups. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
orthogonal $\sigma $-completeness |
| Keyword:
|
direct factor |
| MSC:
|
06F15 |
| MSC:
|
20F60 |
| idZBL:
|
Zbl 1012.06019 |
| idMR:
|
MR1940067 |
| . |
| Date available:
|
2009-09-24T10:57:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127772 |
| . |
| Reference:
|
[1] J. Jakubík: Cardinal properties of lattice ordered groups.Fund. Math. 74 (1972), 85–98. MR 0302528, 10.4064/fm-74-2-85-98 |
| Reference:
|
[2] J. Jakubík: Cantor-Bernstein theorem for lattice ordered groups.Czechoslovak Math. J. 22(97) (1972), 159–175. MR 0297666 |
| Reference:
|
[3] J. Jakubík: On complete lattice ordered groups with strong units.Czechoslovak Math. J. 46(121) (1996), 221–230. MR 1388611 |
| Reference:
|
[4] J. Jakubík: Cantor-Bernstein theorem for $MV$-algebras.Czechoslovak Math. J. 49(124) (1999), 517–526. MR 1708370, 10.1023/A:1022467218309 |
| Reference:
|
[5] J. Jakubík: Convex isomorphisms of archimedean lattice ordered groups.Mathware Soft Comput. 5 (1998), 49–56. MR 1632739 |
| Reference:
|
[6] R. Sikorski: A generalization of theorem of Banach and Cantor-Bernstein.Coll. Mat. 1 (1948), 140–144. MR 0027264 |
| Reference:
|
[7] R. Sikorski: Boolean algebras.Second edition, Springer Verlag, Berlin, 1964. Zbl 0123.01303, MR 0126393 |
| Reference:
|
[8] F. Šik: To the theory of lattice ordered groups.Czechoslovak Math. J. 6(81) (1956), 1–25. (Russian) |
| Reference:
|
[9] A. De Simone, D. Mundici and M. Navara: A Cantor-Bernstein theorem for $\sigma $-complete $MV$-algebras.(Preprint). |
| Reference:
|
[10] A. Tarski: Cardinal Algebras.Oxford University Press, New York, London, 1949. Zbl 0041.34502, MR 0029954 |
| . |
