Cantor extension of a half lineary cyclically ordered group

• Autorzy: Štefan Černák
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 20F60: Ordered groups \SeeMainly{}
• 06F15: Ordered groups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 31-46

Daty

wydano

2001

poprawiono

1996-04-30

otrzymano

1999-06-07

Twórcy

autor

Štefan Černák

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1025