Convergence with a regulator in directed groups

• Autorzy: Štefan Černák
• Języki publikacji: EN

Abstrakty

EN

There is defined and studied a convergence with a fixed regulator u in directed groups. A u-Cauchy completion of an integrally closed directed group is constructed.

Słowa kluczowe

EN

convergent sequence; fundamental sequence; Cauchy completion; integrally closed directed group; convergence regulator; vector lattice

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: 2004
• Tom: 24
• Numer: 2
• Strony: 211-223

Daty

wydano

2004

otrzymano

2004-04-14

poprawiono

2004-12-27

Twórcy

autor

Štefan Černák

• Department of Mathematics, Faculty of Civil Engineering, Technical University, Vysokoškolská 4, SK-042 02 Košice, Slovakia
• Mathematical Institute, Slovak Akademy of Sciences, Grešaková 6, SK-04001 Košice, Slovakia

Bibliografia

• [1] S. Černák and J. Lihova, Convergence with a regulator in lattice ordered groups, Tatra Mt. Math. Publ. to appear.
• [2] M.R. Darnel, Theory of Lattice-Ordered Groups, M. Dekker, Inc., New York 1995
• [3] L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press., Oxford 1963.
• [4] A.M.W. Glass, Partially Ordered Groups, World Scientific Publ. Co., River Edge, NJ, 1999.
• [5] W.A.J. Luxemburg and A. C. Zaanen, Riesz Spaces, vol. I, North-Holland, Amsterdam-London 1971.
• [6] B.Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff Sci. Publ., Groningen 1967 (The original Russian edition in: Fizmatgiz, Moskow 1961).

Identyfikatory

DOI

10.7151/dmgaa.1086