×

zbMATH — the first resource for mathematics

Subgroups and hulls of Specker lattice-ordered groups. (English) Zbl 0978.06011
Summary: It is 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 a 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.

MSC:
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
06F25 Ordered rings, algebras, modules
46A40 Ordered topological linear spaces, vector lattices
12J15 Ordered fields
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] P. F. Conrad: The hulls of representable \(\ell \)-groups and \(f\)-rings. J. Austral. Math. Soc. 16 (1973), 385-415. · Zbl 0275.06025
[2] P. F. Conrad: Epi-archimedean \(\ell \)-groups. Czechoslovak Math. J. 24 (1974), 192-218. · Zbl 0319.06009
[3] P. F. Conrad: The hulls of semiprime rings. Czechoslovak Math. J. 28 (1978), 59-86. · Zbl 0419.16002
[4] P. F. Conrad and M. R. Darnel: Lattice-ordered groups whose lattices determine their additions. Trans. Amer. Math. Soc. 330 (1992), 575-598. · Zbl 0756.06009
[5] P. F. Conrad and M. R. Darnel: Countably valued lattice-ordered groups. Algebra Universalis 36 (1996), 81-107. · Zbl 0870.06012
[6] P. F. Conrad and M. R. Darnel: Generalized Boolean algebras in lattice-ordered groups. Order 14 (1998), 295-319. · Zbl 0919.06009
[7] P. F. Conrad and J. Martinez: Signatures and \(S\)-discrete lattice-ordered groups. Algebra Universalis 29 (1992), 521-545. · Zbl 0767.06015
[8] P. F. Conrad and D. McAlister: The completion of a \(\ell \)-group. J. Austral. Math. Soc. 9 (1969), 182-208. · Zbl 0172.31601
[9] M. R. Darnel: The Theory of Lattice-ordered Groups. Marcel Dekker, , 1995. · Zbl 0810.06016
[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. · Zbl 0819.06014
[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
[12] J. Jakubík: Lattice-ordered groups with unique addition must be archimedean. Czechoslovak Math. J. 41(116) (1991), 559-603. · Zbl 0756.06011
[13] S. Lin: Some Theorems on Lattice-ordered Groups. Dissertation, University of Kansas, 1991.
[14] C. Nobeling: Verallgemeinerung eines Satzes von Herrn E. Specker. Invent. Math. 6 (1968), 41-55. · Zbl 0176.29801
[15] S. Wolfenstein: Contribution à l’étude des groupes reticulés: Extensions archimédiennes, Groupes à valeurs normales. Thesis, Sci. Math. Paris, 1970.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.