| Title:
|
Subgroups and hulls of Specker lattice-ordered groups (English) |
| Author:
|
Conrad, Paul F. |
| Author:
|
Darnel, Michael R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
395-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
lattice-ordered groups |
| Keyword:
|
$f$-rings |
| Keyword:
|
Specker groups |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| MSC:
|
06F25 |
| MSC:
|
12J15 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 0978.06011 |
| idMR:
|
MR1844319 |
| . |
| Date available:
|
2009-09-24T10:43:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127656 |
| . |
| Reference:
|
[1] P. F. Conrad: The hulls of representable $\ell $-groups and $f$-rings.J. Austral. Math. Soc. 16 (1973), 385–415. MR 0344173, 10.1017/S1446788700015391 |
| Reference:
|
[2] P. F. Conrad: Epi-archimedean $\ell $-groups.Czechoslovak Math. J. 24 (1974), 192–218. MR 0347701 |
| Reference:
|
[3] P. F. Conrad: The hulls of semiprime rings.Czechoslovak Math. J. 28 (1978), 59–86. Zbl 0419.16002, MR 0463223 |
| Reference:
|
[4] P. F. Conrad and M. R. Darnel: Lattice-ordered groups whose lattices determine their additions.Trans. Amer. Math. Soc. 330 (1992), 575–598. MR 1031238, 10.1090/S0002-9947-1992-1031238-0 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] P. F. Conrad and D. McAlister: The completion of a $\ell $-group.J. Austral. Math. Soc. 9 (1969), 182–208. MR 0249340, 10.1017/S1446788700005760 |
| Reference:
|
[9] M. R. Darnel: The Theory of Lattice-ordered Groups.Marcel Dekker, , 1995. MR 1304052 |
| Reference:
|
[10] M. R. Darnel, M. Giraudet and S. H. McCleary: Uniqueness of the group operation on the lattice of order-automorphisms of the real line.Algebra Universalis 33 (1995), 419–427. MR 1322783, 10.1007/BF01190709 |
| Reference:
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[11] W. C. Holland: Partial orders of the group of automorphisms of the real line.Proc. International Conf. on Algebra, Part 1 (Novosibirsk, 1989), pp. 197–207. Zbl 0766.06015, MR 1175773 |
| Reference:
|
[12] J. Jakubík: Lattice-ordered groups with unique addition must be archimedean.Czechoslovak Math. J. 41(116) (1991), 559–603. MR 1117808 |
| Reference:
|
[13] S. Lin: Some Theorems on Lattice-ordered Groups.Dissertation, University of Kansas, 1991. |
| Reference:
|
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| Reference:
|
[15] S. Wolfenstein: Contribution à l’étude des groupes reticulés: Extensions archimédiennes, Groupes à valeurs normales.Thesis, Sci. Math. Paris, 1970. |
| . |
