Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 28
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Heubo-Kwegna, Olivier A. Olberding, Bruce and Reinhart, Andreas 2016. Group-theoretic and topological invariants of completely integrally closed Prüfer domains. Journal of Pure and Applied Algebra, Vol. 220, Issue. 12, p. 3927.
    BEZHANISHVILI, GURAM MORANDI, PATRICK J. and OLBERDING, BRUCE 2013. DEDEKIND COMPLETIONS OF BOUNDED ARCHIMEDEAN ℓ-ALGEBRAS. Journal of Algebra and Its Applications, Vol. 12, Issue. 01, p. 1250139.
    Knox, Michelle L. and McGovern, Warren Wm. 2009. Feebly projectable ℓ-groups. Algebra universalis, Vol. 62, Issue. 1, p. 91.
    Knox, Michelle L. and McGovern, Warren Wm. 2008. Rigid extensions of ℓ-groups of continuous functions. Czechoslovak Mathematical Journal, Vol. 58, Issue. 4, p. 993.
    McGovern, Warren W. 2007. Bézout SP-Domains. Communications in Algebra, Vol. 35, Issue. 5, p. 1777.
    Jakubík, Ján 2002. Torsion classes of Specker lattice ordered groups. Czechoslovak Mathematical Journal, Vol. 52, Issue. 3, p. 469.
    Conrad, Paul F. and Darnel, Michael R. 2001. Subgroups and Hulls of Specker Lattice-Ordered Groups. Czechoslovak Mathematical Journal, Vol. 51, Issue. 2, p. 395.
    Jakubík, Ján 1999. Cantor-Bernstein theorem for MV-algebras. Czechoslovak Mathematical Journal, Vol. 49, Issue. 3, p. 517.
    McGovern, Warren Wm. 1998. Singular f-rings which are α-G.C.D. rings. Topology and its Applications, Vol. 88, Issue. 3, p. 199.
    Darnel, Michael R. 1993. Varieties minimal over representable varieties of lattice-ordered groups. Communications in Algebra, Vol. 21, Issue. 8, p. 2637.
    Conrad, Paul and Martinez, Jorge 1992. Signatures andS-discrete lattice-ordered groups. Algebra Universalis, Vol. 29, Issue. 4, p. 521.
    Conrad, Paul and Martinez, Jorge 1990. Very large subgroups of a lattice-ordered group. Communications in Algebra, Vol. 18, Issue. 7, p. 2063.
    Conrad, Paul and Martinez, Jorge 1990. Complemented lattice-ordered groups. Indagationes Mathematicae, Vol. 1, Issue. 3, p. 281.
    Ton, Dao-Rong 1989. Epicomplete archimedean lattice-ordered groups. Bulletin of the Australian Mathematical Society, Vol. 39, Issue. 02, p. 277.
    Daorong, Tong 1986. The construction theorem of an ArchimedeanI-group. Acta Mathematica Sinica, Vol. 2, Issue. 4, p. 292.
    Tsinakis, Constantine 1985. Projectable and strongly projectable lattice-ordered groups. Algebra Universalis, Vol. 20, Issue. 1, p. 57.
    Anderson, Marlow and Conrad, Paul 1981. Epicompletel-groups. Algebra Universalis, Vol. 12, Issue. 1, p. 224.
    Ball, Richard N. 1981. Algebra Carbondale 1980. Vol. 848, Issue. , p. 208.
    Anderson, Marlow and Kenny, Otis 1980. The root system of primes of a Hahn group. Journal of the Australian Mathematical Society, Vol. 29, Issue. 01, p. 17.
    Anderson, Marlow Conrad, Paul and Kenny, Otis 1977. Splitting properties in Archimedean l-groups. Journal of the Australian Mathematical Society, Vol. 23, Issue. 02, p. 247.
    Download full list
    ×
  • Access

The Completion of a Lattice Ordered Group

  • Paul Conrad (a1) and Donald McAlister (a1)
Extract

A lattice ordered group(‘l-group’) is called complete if each set of elements that is bounded above has a least upper bound (and dually). A complete l-group is archimedean and hence abelian, and each archimedean l-group has a completion in the sense of the following theorem.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The Completion of a Lattice Ordered Group
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      The Completion of a Lattice Ordered Group
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      The Completion of a Lattice Ordered Group
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Society 1969
References
Hide All
[1]Banaschewski, B., ‘On lattice ordered groups’. Fundamenta Math. 55 (1964) 113–123.
[2]Bernau, S. J., ‘Unique representation of archimedean lattice groups and normal archimedean lattice rings’. Proc. London Math. Soc. 15 (1965), 599–631.
[3]Bernau, S. J., ‘Orthocompletion of lattice groups’. Proc. London Math. Soc. 16 (1966), 107–130.
[4]Birkhoff, G., ‘Lattice theory’. American Math. Soc. Colloquium Pub. 25, (1948).
[5]Byrd, R., Tulane Dissertation (1966).
[6]Byrd, R., ‘Complete distributivity in lattice ordered groups’. Pacific J. Math. 20 (1967), 423–432.
[7]Conrad, P., ‘Some structure theorems for lattice ordered groups’. Trans. American Math. Soc. 99 (1961), 212–240.
[8]Conrad, P., ‘The relationship between the radical of a lattice-ordered group and complete distributivity’. Pacific J. Math. 14 (1964), 493–499.
[9]Conrad, P., ‘The lattice of all convex l-subgroups of a lattice ordered group’. Czech. Math. J. 15 (1965), 101–123.
[10]Conrad, P., ‘Archimedean extensions of lattice ordered groups’. J. Indian Math. Soc. 30 (1966), 131–160.
[11]Conrad, P., ‘Lateral completions of lattice ordered groups’. (To appear). Proc. London Math. Soc.
[12]Fuchs, L., Partially Ordered Algebraic Systems. (Pergamon Press. 1963).
[13]Iwasawa, K., ‘On the structure of conditionally complete lattice-groups’. Japan J. Math. 18 (1943), 777–789.
[14]Jaffard, P., ‘Sur le spectre d'un groupe réticule et l'unicité des réalisations irréducibles’. Ann. Univ. Lyon, 22 (1950), 43–47.
[15]Jakubik, J., ‘Representations and extensions of l-groups’. Czech. Math. J. 13 (1963), 267–283.
[16]Johnson, D. G. and Kist, J. E., ‘Complemented ideals and extremely disconnected spaces’. Archiv der Math. 12 (1961), 349–354.
[17]Johnson, D. G. and Kist, J. E., ‘Prime ideals in vector lattices’. Canadian J. Math. 14 (1962), 512–528.
[18]Lorenz, K., ‘Über Strukturverbande von Verbandsgruppen’. Acta. Math. Soc. Hungary. 13 (1962), 55–67.
[19]MacNeille, H., ‘Partially ordered sets’. Trans American Math. Soc. 42 (1937), 416–460.
[20]Topping, D., ‘Some homological pathology in vector lattices. Canadian J. Math. 17 (1963), 411–428.
[21]Weinberg, E., ‘Completely distributive lattice ordered groups’. Pacific J. Math. 12 (1962), 1131–1137.
[22]Weinberg, E., ‘Free lattice ordered abelian groups’. Math. Annalen 151 (1963), 187–189.
[23]Weinberg, E., ‘Free lattice ordered abelian groups, II’. Math. Annalen 159 (1965), 217–222.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 64 *
Loading metrics...

Abstract views

Total abstract views: 116 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×