Cantor extension of a half lineary cyclically ordered group

Štefan Černák

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 1, page 31-46
  • ISSN: 1509-9415

Abstract

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Convergent and fundamental sequences are studied in a half linearly cyclically ordered group G with the abelian increasing part. The main result is the construction of the Cantor extension of G.

How to cite

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Štefan Černák. "Cantor extension of a half lineary cyclically ordered group." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 31-46. <http://eudml.org/doc/287732>.

@article{ŠtefanČernák2001,
abstract = {Convergent and fundamental sequences are studied in a half linearly cyclically ordered group G with the abelian increasing part. The main result is the construction of the Cantor extension of G.},
author = {Štefan Černák},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {convergent sequence; fundamental sequence; C-complete half lc-group; Cantor extension of a half lc-group; half -group; Cantor extension; -completeness},
language = {eng},
number = {1},
pages = {31-46},
title = {Cantor extension of a half lineary cyclically ordered group},
url = {http://eudml.org/doc/287732},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Štefan Černák
TI - Cantor extension of a half lineary cyclically ordered group
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 31
EP - 46
AB - Convergent and fundamental sequences are studied in a half linearly cyclically ordered group G with the abelian increasing part. The main result is the construction of the Cantor extension of G.
LA - eng
KW - convergent sequence; fundamental sequence; C-complete half lc-group; Cantor extension of a half lc-group; half -group; Cantor extension; -completeness
UR - http://eudml.org/doc/287732
ER -

References

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  1. [1] S. Cernák, Cantor extension of an abelian cyclically ordered group, Math. Slovaca 39 (1989), 31-41. Zbl0667.06010
  2. [2] C.J. Everett, Sequence completion of lattice moduls, Duke Math. J. 11 (1944), 109-119. Zbl0060.06301
  3. [3] M. Giraudet and F. Lucas, Groupe a moitié ordonnés, Fund. Math. 139 (1991), 75-89. 
  4. [4] J. Jakubík and G. Pringerová, Representations of cyclically ordered groups, Casopis pest. Mat. 113 (1988), 184-196. Zbl0654.06016
  5. [5] J. Jakubík and G. Pringerová, Radical classes of cyclically ordered groups, Math. Slovaca 38 (1988), 255-268. Zbl0662.06004
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  8. [8] J. Jakubík, On half cyclically ordered groups, Czechoslovak Math. J. (toappear). Zbl1010.06013
  9. [9] V. Novák, Cuts in cyclically ordered sets, Czechoslovak Math. J. 34 (1984), 322-333. Zbl0551.06002
  10. [10] V. Novák and M. Novotný, On representations of cyclically ordered sets, Czechoslovak Math. J. 39 (1989), 127-132. Zbl0676.06010
  11. [11] A. Quilot, Cyclic orders, European J. Combin. 10 (1989), 477-488. Zbl0692.05059
  12. [12] L. Rieger, On ordered and cyclically ordered groups I., II.,III, Vestník Král. Ceske spol. Nauk (Czech), 1946, 1-31; 1947, 1-33; 1948, 1-26. 
  13. [13] S. Świerczkowski, On cyclically ordered groups, Fund. Math. 47 (1959), 161-166. Zbl0096.01501
  14. [14] D.R. Ton, Torsion classes and torsion prime selectors of hl-groups, Math. Slovaca 50 (2000), 31-40. Zbl0955.06010

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