Sequential convergences on free lattice ordered groups

Ján Jakubík

Mathematica Bohemica (1992)

  • Volume: 117, Issue: 1, page 48-54
  • ISSN: 0862-7959

Abstract

top
In this paper the partially ordered set Conv G of all sequential convergences on G is investigated, where G is either a free lattice ordered group or a free abelian lattice ordered group.

How to cite

top

Jakubík, Ján. "Sequential convergences on free lattice ordered groups." Mathematica Bohemica 117.1 (1992): 48-54. <http://eudml.org/doc/29383>.

@article{Jakubík1992,
abstract = {In this paper the partially ordered set Conv $G$ of all sequential convergences on $G$ is investigated, where $G$ is either a free lattice ordered group or a free abelian lattice ordered group.},
author = {Jakubík, Ján},
journal = {Mathematica Bohemica},
keywords = {free lattice-ordered group; compatible sequential convergences; atom; free abelian lattice ordered group; sequential convergence; free lattice-ordered group; compatible sequential convergences; atom},
language = {eng},
number = {1},
pages = {48-54},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sequential convergences on free lattice ordered groups},
url = {http://eudml.org/doc/29383},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Jakubík, Ján
TI - Sequential convergences on free lattice ordered groups
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 1
SP - 48
EP - 54
AB - In this paper the partially ordered set Conv $G$ of all sequential convergences on $G$ is investigated, where $G$ is either a free lattice ordered group or a free abelian lattice ordered group.
LA - eng
KW - free lattice-ordered group; compatible sequential convergences; atom; free abelian lattice ordered group; sequential convergence; free lattice-ordered group; compatible sequential convergences; atom
UR - http://eudml.org/doc/29383
ER -

References

top
  1. M. Anderson T. Feil, Lattice-Ordered Groups, An Introduction, Reidel Publ., Dordrecht, 1988. (1988) MR0937703
  2. S. Bernau, Free abelian lattice groups, Math. Ann. 150(1969), 48-59. (1969) Zbl0157.36801MR0241340
  3. G. Birkhoff, Lattice Theory, Third Edition, Providence, 1967. (1967) Zbl0153.02501MR0227053
  4. P. Conrad, 10.1007/BF01431159, Math. Ann. 190 (1971), 306-312. (190) MR0281667DOI10.1007/BF01431159
  5. P. Conrad, 10.1016/0021-8693(70)90024-4, J. Algebra 16 (1970), 191-203. (1970) Zbl0213.31502MR0270992DOI10.1016/0021-8693(70)90024-4
  6. P. Conrad, Lattice-Ordered Groups, Tulane Lecture Notes; New Orleans, 1970. (1970) Zbl0258.06011
  7. R. Frič F. Zanolin, Sequential convergence in free groups, Rend. Ist. Matem. Univ. Trieste 18 (1986), 200-218. (1986) MR0928331
  8. M. Harminc, Sequential convergences on abelian lattice-ordered groups, Convergence Structures 1984. Mathematical Research, Band 24, Akademie-Verlag, Berlin, 1985, pp. 153-158. (1984) MR0835480
  9. M. Harminc, The cardinality of the system of all sequential convergences on an abelian lattice ordered group, Czechoslovak Math. J. 31 (1987), 533-546. (1987) MR0913986
  10. M. Harminc, Sequential convergences on lattice ordered groups, Czechoslov. Math. J 39 (1989), 232-238. (1989) MR0992130
  11. M. Harminc, Convergences on lattice ordered groups, Dissertation, Math. Inst. Slovak Acad. Sci, 1986. (In Slovak.) (1986) 
  12. M. Harminc J. Jakubík, Maximal convergences and minimal proper convergences in l-groups, Czechoslov. Math. J. 39 (1989), 631-640. (1989) MR1017998
  13. J. Jakubík, Convergences and complete distributivity of lattice ordered groups, Math. Slovaca 38 (1988), 269-272. (1988) MR0977905
  14. J. Jakubík, Lattice ordered groups having a largest convergence, Czechoslov. Math. J. 39 (1989), 717-729. (1989) MR1018008
  15. B. M. Koпытов, Рещеточно упорядоченные группы, Mocквa, 1984. (1984) Zbl1063.82528
  16. J. Novák, On a free convergence group., Proc. Conf. on Convergence Structures, Lawton, Oklahoma, 1980, pp. 97-102. (1980) MR0605123
  17. E. C. Weinberg, 10.1007/BF01398232, Math. Ann. 151 (1963), 187-199. (1963) Zbl0114.25801MR0153759DOI10.1007/BF01398232
  18. E. C. Weinberg, 10.1007/BF01362439, Math. Ann. 159 (1965), 217-222. (1965) Zbl0138.26201MR0181668DOI10.1007/BF01362439

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.