Convergence with a regulator in directed groups
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 211-223
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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.
Keywords:
convergent sequence, fundamental sequence, Cauchy completion, integrally closed directed group, convergence regulator, vector lattice
@article{DMGAA_2004_24_2_a4,
author = {\v{C}ern\'ak, \v{S}tefan},
title = {Convergence with a regulator in directed groups},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {211--223},
year = {2004},
volume = {24},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a4/}
}
Černák, Štefan. Convergence with a regulator in directed groups. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 211-223. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a4/
[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).