Previous |  Up |  Next


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:
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


Files Size Format View
CzechMathJ_54-2004-2_21.pdf 321.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo