Subgroups and hulls of Specker lattice-ordered groups

Paul F. Conrad; Michael R. Darnel

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 395-413
  • ISSN: 0011-4642

Abstract

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In this article, it will be shown that every ℓ -subgroup of a Specker ℓ -group has singular elements and that the class of ℓ -groups that are ℓ -subgroups of Specker ℓ -group form a torsion class. Methods of adjoining units and bases to Specker ℓ -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker ℓ -group.

How to cite

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Conrad, Paul F., and Darnel, Michael R.. "Subgroups and hulls of Specker lattice-ordered groups." Czechoslovak Mathematical Journal 51.2 (2001): 395-413. <http://eudml.org/doc/30643>.

@article{Conrad2001,
abstract = {In this article, it will be shown that every $\ell $-subgroup of a Specker $\ell $-group has singular elements and that the class of $\ell $-groups that are $\ell $-subgroups of Specker $\ell $-group form a torsion class. Methods of adjoining units and bases to Specker $\ell $-groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker $\ell $-group.},
author = {Conrad, Paul F., Darnel, Michael R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {lattice-ordered groups; $f$-rings; Specker groups; lattice-ordered groups; -rings; Specker groups},
language = {eng},
number = {2},
pages = {395-413},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subgroups and hulls of Specker lattice-ordered groups},
url = {http://eudml.org/doc/30643},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Conrad, Paul F.
AU - Darnel, Michael R.
TI - Subgroups and hulls of Specker lattice-ordered groups
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 395
EP - 413
AB - In this article, it will be shown that every $\ell $-subgroup of a Specker $\ell $-group has singular elements and that the class of $\ell $-groups that are $\ell $-subgroups of Specker $\ell $-group form a torsion class. Methods of adjoining units and bases to Specker $\ell $-groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker $\ell $-group.
LA - eng
KW - lattice-ordered groups; $f$-rings; Specker groups; lattice-ordered groups; -rings; Specker groups
UR - http://eudml.org/doc/30643
ER -

References

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  1. 10.1017/S1446788700015391, J.  Austral. Math. Soc. 16 (1973), 385–415. (1973) MR0344173DOI10.1017/S1446788700015391
  2. Epi-archimedean ℓ -groups, Czechoslovak Math.  J. 24 (1974), 192–218. (1974) MR0347701
  3. The hulls of semiprime rings, Czechoslovak Math. J. 28 (1978), 59–86. (1978) Zbl0419.16002MR0463223
  4. 10.1090/S0002-9947-1992-1031238-0, Trans. Amer. Math. Soc. 330 (1992), 575–598. (1992) MR1031238DOI10.1090/S0002-9947-1992-1031238-0
  5. 10.1007/BF01192710, Algebra Universalis 36 (1996), 81–107. (1996) MR1397569DOI10.1007/BF01192710
  6. Generalized Boolean algebras in lattice-ordered groups, Order 14 (1998), 295–319. (1998) MR1644504
  7. 10.1007/BF01190779, Algebra Universalis 29 (1992), 521–545. (1992) MR1201177DOI10.1007/BF01190779
  8. 10.1017/S1446788700005760, J.  Austral. Math. Soc. 9 (1969), 182–208. (1969) MR0249340DOI10.1017/S1446788700005760
  9. The Theory of Lattice-ordered Groups, Marcel Dekker, , 1995. (1995) MR1304052
  10. 10.1007/BF01190709, Algebra Universalis 33 (1995), 419–427. (1995) MR1322783DOI10.1007/BF01190709
  11. Partial orders of the group of automorphisms of the real line, Proc. International Conf. on Algebra, Part  1 (Novosibirsk, 1989), pp.  197–207. Zbl0766.06015MR1175773
  12. Lattice-ordered groups with unique addition must be archimedean, Czechoslovak Math.  J. 41(116) (1991), 559–603. (1991) MR1117808
  13. Some Theorems on Lattice-ordered Groups, Dissertation, University of Kansas, 1991. (1991) 
  14. 10.1007/BF01389832, Invent. Math. 6 (1968), 41–55. (1968) MR0231907DOI10.1007/BF01389832
  15. Contribution à l’étude des groupes reticulés: Extensions archimédiennes, Groupes à valeurs normales, Thesis, Sci. Math. Paris, 1970. (1970) 

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