| Title:
|
On some interpolation rules for lattice ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
499-507 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\alpha $ be an infinite cardinal. In this paper we define an interpolation rule $\mathop {\mathrm IR}(\alpha )$ for lattice ordered groups. We denote by $C (\alpha )$ the class of all lattice ordered groups satisfying $\mathop {\mathrm IR}(\alpha )$, and prove that $C (\alpha )$ is a radical class. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
interpolation rule |
| Keyword:
|
radical class |
| MSC:
|
06F15 |
| MSC:
|
20F60 |
| idZBL:
|
Zbl 1080.06028 |
| idMR:
|
MR2059269 |
| . |
| Date available:
|
2009-09-24T11:14:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127906 |
| . |
| Reference:
|
[1] P. F. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[2] P. F. Conrad: $K$-radical classes of lattice ordered groups.In: Proc. Conf. Carbondale (1980), Lecture Notes Math. Vol. 848, 1981, pp. 186–207. Zbl 0455.06010, MR 0613186 |
| Reference:
|
[3] M. R. Darnel: $\sigma $-interpolation lattice-ordered groups.Czechoslovak Math. J. 50 (2000), 1–2. Zbl 1035.06004, MR 1745452, 10.1023/A:1022403616010 |
| Reference:
|
[4] M. R. Darnel and J. Martinez: Radical classes of lattice ordered groups vs. classes of compact spaces.Order 19 (2002), 35–72. MR 1902661, 10.1023/A:1015259615457 |
| Reference:
|
[5] K. R. Goodearl: Partially Ordered Abelian Groups with Interpolation. Math. Surveys and Monographs, No. 20.Amer. Math. Soc., Providence, 1986. MR 0845783 |
| Reference:
|
[6] Ch. W. Holland: Varieties of $\ell $-groups are torsion classes.Czechoslovak Math. J. 29 (1979), 11–12. MR 0518135 |
| Reference:
|
[7] J. Jakubík: Radical mappings and radical classes of lattice ordered groups.Symposia Math. 21 (1977), 451–477. MR 0491397 |
| Reference:
|
[8] J. Jakubík: On some completeness properties for lattice ordered groups.Czechoslovak Math. J. 45 (1995), 253–266. MR 1331463 |
| Reference:
|
[9] N. Ja. Medvedev: On the lattice of radicals of a finitely generated $\ell $-group.Math. Slovaca 33 (1983), 185–188. (Russian) MR 0699088 |
| Reference:
|
[10] R. C. Walker: The Stone-Čech Compactification. Ergebn. Math. 80.Springer-Verlag, Berlin-Heidelberg-New York, 1974. MR 0380698 |
| . |
