ArticleOriginal scientific text

Title

Cantor extension of a half lineary cyclically ordered group

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, Technical University, Vysokoskolská 4, SK-042 02 Kosice, Slovakia

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.

Keywords

convergent sequence, fundamental sequence, C-complete half lc-group, Cantor extension of a half lc-group

Bibliography

  1. S. Cernák, Cantor extension of an abelian cyclically ordered group, Math. Slovaca 39 (1989), 31-41.
  2. C.J. Everett, Sequence completion of lattice moduls, Duke Math. J. 11 (1944), 109-119.
  3. M. Giraudet and F. Lucas, Groupe a moitié ordonnés, Fund. Math. 139 (1991), 75-89.
  4. J. Jakubík and G. Pringerová, Representations of cyclically ordered groups, Casopis pest. Mat. 113 (1988), 184-196.
  5. J. Jakubík and G. Pringerová, Radical classes of cyclically ordered groups, Math. Slovaca 38 (1988), 255-268.
  6. J. Jakubík, On half lattice ordered groups, Czechoslovak Math. J. 46 (1996), 745-767.
  7. J. Jakubík, Lexicographic products of half linearly ordered groups, Czechoslovak Math. J. 51 (2001), 127-138.
  8. J. Jakubík, On half cyclically ordered groups, Czechoslovak Math. J. (toappear).
  9. V. Novák, Cuts in cyclically ordered sets, Czechoslovak Math. J. 34 (1984), 322-333.
  10. V. Novák and M. Novotný, On representations of cyclically ordered sets, Czechoslovak Math. J. 39 (1989), 127-132.
  11. A. Quilot, Cyclic orders, European J. Combin. 10 (1989), 477-488.
  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. S. Świerczkowski, On cyclically ordered groups, Fund. Math. 47 (1959), 161-166.
  14. D.R. Ton, Torsion classes and torsion prime selectors of hl-groups, Math. Slovaca 50 (2000), 31-40.
Pages:
31-46
Main language of publication
English
Received
1999-06-07
Accepted
1996-04-30
Published
2001
Exact and natural sciences