Completion of a half linearly cyclically ordered group

• Autorzy: Štefan Černák
• Języki publikacji: EN

Abstrakty

EN

The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.

Słowa kluczowe

EN

dedekind cut; cyclically ordered group; lc-group; half lc-group; completion 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: 2002
• Tom: 22
• Numer: 1
• Strony: 5-23

Daty

wydano

2002

otrzymano

2001-06-06

Twórcy

autor

Štefan Černák

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

Bibliografia

• [1] Š. Černák, On the completion of cyclically ordered groups, Math. Slovaca 41 (1991), 41-49.
• [2] M. Giraudet and F. Lucas, Groupes à moitié ordonnés, Fund. Math. 139 (1991), 75-89.
• [3] J. Jakubík, On half cyclically ordered groups, Czechoslovak Math. J. (to appear).
• [4] J. Jakubík and Š. Černák, Completion of a cyclically ordered group, Czechoslovak Math. J. 37 (112) (1987), 157-174.
• [5] V. Novák, Cuts in cyclically ordered sets, Czechoslovak Math. J. 34 (109) (1984), 322-333.
• [6] V. Novák and M. Novotný, On completion of cyclically ordered sets, Czechoslovak Math. J. 37 (112) (1987), 407-414.
• [7] A. Quilliot, Cyclic orders, Europan J. Combin. 10 (1989), 477-488.
• [8] L. Rieger, On ordered and cyclically ordered groups. I, II, and III, (Czech), Věstník Královské České Společnosti Nauk. Třida Matemat.-Přirodovĕd. 1946, no. 6, p. 1-31, 1947, no 1, p. 1-33, 1948, no. 1, p. 1-26.
• [9] S. Świerczkowski, On cyclically ordered groups, Fundamenta Math. 47 (1959), 161-166.

Identyfikatory

DOI

10.7151/dmgaa.1043