On some interpolation rules for lattice ordered groups

Ján Jakubík

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 2, page 499-507
  • ISSN: 0011-4642

Abstract

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Let α be an infinite cardinal. In this paper we define an interpolation rule I R ( α ) for lattice ordered groups. We denote by C ( α ) the class of all lattice ordered groups satisfying I R ( α ) , and prove that C ( α ) is a radical class.

How to cite

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Jakubík, Ján. "On some interpolation rules for lattice ordered groups." Czechoslovak Mathematical Journal 54.2 (2004): 499-507. <http://eudml.org/doc/30878>.

@article{Jakubík2004,
abstract = {Let $\alpha $ be an infinite cardinal. In this paper we define an interpolation rule $\mathop \{\mathrm \{I\}R\}(\alpha )$ for lattice ordered groups. We denote by $C (\alpha )$ the class of all lattice ordered groups satisfying $\mathop \{\mathrm \{I\}R\}(\alpha )$, and prove that $C (\alpha )$ is a radical class.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {lattice ordered group; interpolation rule; radical class; lattice-ordered group; interpolation rule; radical class},
language = {eng},
number = {2},
pages = {499-507},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some interpolation rules for lattice ordered groups},
url = {http://eudml.org/doc/30878},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Jakubík, Ján
TI - On some interpolation rules for lattice ordered groups
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 499
EP - 507
AB - Let $\alpha $ be an infinite cardinal. In this paper we define an interpolation rule $\mathop {\mathrm {I}R}(\alpha )$ for lattice ordered groups. We denote by $C (\alpha )$ the class of all lattice ordered groups satisfying $\mathop {\mathrm {I}R}(\alpha )$, and prove that $C (\alpha )$ is a radical class.
LA - eng
KW - lattice ordered group; interpolation rule; radical class; lattice-ordered group; interpolation rule; radical class
UR - http://eudml.org/doc/30878
ER -

References

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  2. K -radical classes of lattice ordered groups, In: Proc. Conf. Carbondale (1980), Lecture Notes Math. Vol. 848, 1981, pp. 186–207. (1981) Zbl0455.06010MR0613186
  3. 10.1023/A:1022403616010, Czechoslovak Math.  J. 50 (2000), 1–2. (2000) Zbl1035.06004MR1745452DOI10.1023/A:1022403616010
  4. 10.1023/A:1015259615457, Order 19 (2002), 35–72. (2002) MR1902661DOI10.1023/A:1015259615457
  5. Partially Ordered Abelian Groups with Interpolation. Math. Surveys and Monographs, No.  20, Amer. Math. Soc., Providence, 1986. (1986) MR0845783
  6. Varieties of ℓ -groups are torsion classes, Czechoslovak Math.  J. 29 (1979), 11–12. (1979) MR0518135
  7. Radical mappings and radical classes of lattice ordered groups, Symposia Math. 21 (1977), 451–477. (1977) MR0491397
  8. On some completeness properties for lattice ordered groups, Czechoslovak Math.  J. 45 (1995), 253–266. (1995) MR1331463
  9. On the lattice of radicals of a finitely generated  ℓ -group, Math. Slovaca 33 (1983), 185–188. (Russian) (1983) MR0699088
  10. The Stone-Čech Compactification. Ergebn. Math.  80, Springer-Verlag, Berlin-Heidelberg-New York, 1974. (1974) MR0380698

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