On absolute retracts and absolute convex retracts in some classes of l-groups

Ján Jakubík

Discussiones Mathematicae - General Algebra and Applications (2003)

  • Volume: 23, Issue: 1, page 19-30
  • ISSN: 1509-9415

Abstract

top
By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.

How to cite

top

Ján Jakubík. "On absolute retracts and absolute convex retracts in some classes of l-groups." Discussiones Mathematicae - General Algebra and Applications 23.1 (2003): 19-30. <http://eudml.org/doc/287617>.

@article{JánJakubík2003,
abstract = {By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.},
author = {Ján Jakubík},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {l-group; absolute retract; absolute convex retract; archimedean l-group; complete l-group; orthogonal completeness; archimedean -group; complete -group},
language = {eng},
number = {1},
pages = {19-30},
title = {On absolute retracts and absolute convex retracts in some classes of l-groups},
url = {http://eudml.org/doc/287617},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Ján Jakubík
TI - On absolute retracts and absolute convex retracts in some classes of l-groups
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2003
VL - 23
IS - 1
SP - 19
EP - 30
AB - By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.
LA - eng
KW - l-group; absolute retract; absolute convex retract; archimedean l-group; complete l-group; orthogonal completeness; archimedean -group; complete -group
UR - http://eudml.org/doc/287617
ER -

References

top
  1. [1] P. Conrad, Lattice Ordered Groups, Tulane University, New Orleans, LA, 1970. Zbl0258.06011
  2. [2] P. Conrad, The essential closure of an archimedean lattice-ordered group, Duke Math. J. 38 (1971), 151-160. Zbl0216.03104
  3. [3] P. Halmos, Injective and projective Boolean algebras, 'Lattice Theory' (R.P. Dilworth, editor), Amer. Math. Soc., Providence, RI,1961, 114-122. 
  4. [4] J. Jakubík, Splitting property of lattice ordered groups, Czechoslovak Math. J. 24 (1974), 257-269. Zbl0327.06013
  5. [5] J. Jakubík, Orthogonal hull of a strongly projectable lattice ordered group, Czechoslovak Math. J. 28 (1978), 484-504. Zbl0391.06014
  6. [6] J. Jakubík, Retracts of abelian cyclically ordered groups, Archivum Math. (Brno) 25 (1989), 13-18. Zbl0712.06013
  7. [7] J. Jakubík, Retracts of abelian lattice ordered groups, Czechoslovak Math. J. 39 (1989), 477-489. Zbl0691.06009
  8. [8] J. Jakubík, Retract varieties of lattice ordered groups, Czechoslovak Math. J. 40 (1990), 104-112. Zbl0705.06011

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.