The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups

References

[1] ARON, E. R.: Embedding lattice-ordered algebras in uniformly closed algebras. University of Rochester Dissertation, 1971.Search in Google Scholar

[2] ARON, E. R.-HAGER, A. W.: Convex vector lattices and l-algebras, Topology Appl. 12 (1981), 1-10.10.1016/0166-8641(81)90024-9Search in Google Scholar

[3] BALL, R. N.-HAGER, A.W.: Characterization of epimorphism in Archimedean latticeordered groups and vector lattices. In: Lattice Ordered Groups. Math. Appl. 48, Kluwer Acad. Publ., Dordrecht, pp. 175-205, 1989.Search in Google Scholar

[4] BALL, R. N.-HAGER, A. W.: Epicompletion of Archimedean l-groups and vector lattices with weak unit, J. Austral. Math. Soc. Ser. A 48 (1990), 25-56.10.1017/S1446788700035175Search in Google Scholar

[5] BALL, R. N.-HAGER, A. W.: Epicomplete Archimedean l-groups and vector lattices, Trans. Amer. Mat. Soc. 322 (1990), 459-478.Search in Google Scholar

[6] BALL, R. N.-HAGER, A. W.: On the localic Yosida representation of an Archimedean lattice ordered group with weak order unit. In: Proceedings of the Conference on Locales and Topological groups (Curacao, 1989). J. Pure Appl. Algebra 70 (1991), 17-43.Search in Google Scholar

[7] BALL, R. N.-HAGER, A. W.: Algebraic extensions of an Archimedean lattice-ordered group I, J. Pure Appl. Algebra 85 (1993), 1-20.10.1016/0022-4049(93)90167-RSearch in Google Scholar

[8] BALL, R. N.-HAGER, A. W.: Algebraic extensions of an Archimedean lattice-ordered group II, J. Pure Appl. Algebra 138 (1999), 197-204.10.1016/S0022-4049(99)00018-3Search in Google Scholar

[9] BALL, R. N.-HAGER, A. W.: The relative uniform density of the continuous functions in the Baire functions, and of a divisible l-group in any epicompletion, Topology Appl. 97 (1999), 109-126 (Special issue in honor of W. M. Comfort, Cura¸cao, 1996).Search in Google Scholar

[10] BALL, R. N.-HAGER, A. W.: A new characterization of the continuous functions on a locale, Positivity 10 (2006), 165-199.10.1007/s11117-005-5826-5Search in Google Scholar

[11] BIGARD, A.-KEIMEL, K.-WOLFENSTEIN, S.: Groupes et anneaux r´eticul´es. Lecture Notes in Math. 608, Springer Verlag, Berlin-New York, 1977.10.1007/BFb0067004Search in Google Scholar

[12] CHITTENDEN, E. W.: Relatively uniform convergence and the classification of functions, Trans. Amer. Math. Soc. 23 (1922), 1-15.10.1090/S0002-9947-1922-1501185-1Search in Google Scholar

[13] DARNEL, M. R.: Theory of Lattice-ordered Groups, Monogr. Textb. in Pure Appl. Math. 187, Marcel Dekker, Inc., New York, 1995.Search in Google Scholar

[14] DASHIELL, F. K., JR.: A theorem on C∗-embedding, Proc. Amer. Math. Soc. 69 (1978), 359-360.Search in Google Scholar

[15] FINE, N. J.-GILLMAN, L.-LAMBEK, J.: Rings of quotients of rings of functions, McGill Univ. Press, Montreal-Quebec, 1966.Search in Google Scholar

[16] GILLMAN, L.-JERISON, M.: Rings of Continuous Functions, Van Nostrand, Princeton, NJ, 1960; Grad. Texts in Math. 43, Springer, Berlin, 1976.10.1007/978-1-4615-7819-2Search in Google Scholar

[17] HAGER, A. W.: Algebraic closures of l-groups of continuous functions. In: Rings Continuous Functions (C. Aull, ed.). Lecture Notes in Pure Appl. Math. 95, Dekker, New York, 1985, pp. 165-194.Search in Google Scholar

[18] HAGER, A. W.-JOHNSON, D. G.: Relative uniform completeness and order-convex representations of archimedean l-groups and f-rings, Topology Appl. 158 (2011), 1866-1874.10.1016/j.topol.2011.06.023Search in Google Scholar

[19] HAGER, A. W.-MADDEN, J. J.: Essential reflections versus minimal embeddings, J. Pure Appl. Algebra 37 (1985), 27-32.10.1016/0022-4049(85)90084-2Search in Google Scholar

[20] HAGER, A. W.-MARTINEZ, J.: α-projectable and laterally α-complete archimedean lattice-ordered groups, SINET: Ethiop. J. Sci. Suppl. 19 1996, 73-84.Search in Google Scholar

[21] HAGER, A. W.-MARTINEZ, J.: The laterally σ-complete reflection of an Archimedean lattice-ordered group. In: Ordered Algebraic Structures (Cura¸cao, 1995), Kluwer Acad. Publ., Dordrecht, 1997, pp. 217-236.Search in Google Scholar

[22] HAGER, A. W.-MARTINEZ, J.: More on the laterally σ-complete reflection of an Archimedean lattice-ordered group, Order 15 (1998/99), 247-260.Search in Google Scholar

[23] HAGER, A. W.-MARTINEZ, J.: C-epic compactifications, Topology Appl. 117 (2002), 113-138.10.1016/S0166-8641(00)00119-XSearch in Google Scholar

[24] HAGER, A. W.-ROBERTSON, L. C.: Representing and ringifying a Riesz space. In: Convegno sulle Misure su Gruppi e su Spazi Vettoriali, Convegno sui Gruppi e Anelli Ordinati, INDAM, Rome, 1975. Symposia Math. XXI, Academic Press, London, 1977, pp. 411-431.Search in Google Scholar

[25] HAGER, A. W.-ROBERTSON, L. C.: On the embedding into a ring of an Archimedean l-group, Canad. J. Math. 31 (1979), 1-8.10.4153/CJM-1979-001-5Search in Google Scholar

[26] HENRIKSEN, M.-ISBELL, J. R.-JOHNSON, D. G.: Residue class fields of latticeordered algebras, Fund. Math. 50 (1961), 107-117.10.4064/fm-50-2-107-117Search in Google Scholar

[27] HERRLICH, H.-STRECKER, G.: Category Theory, Allyn and Bacon, Boston, MA, 1973.Search in Google Scholar

[28] ISBELL, J.: Atomless parts of spaces, Math. Scand. 31 (1972), 5-32.10.7146/math.scand.a-11409Search in Google Scholar

[29] ISBELL, J. R.: General Functorial semantics I, Amer. J. Math. 94 (1972), 535-596.10.2307/2374638Search in Google Scholar

[30] JAKUB´IK, J.-ˇCERN´AK, ˇS.: Relatively uniform convergences in archimedean lattice ordered groups, Math. Slovaca 60 (2010), 447-460.10.2478/s12175-010-0024-8Search in Google Scholar

[31] LUXEMBURG, W. A. J.-ZAANEN, A. C.: Riesz spaces. Vol. I. North-Holland Math. Library, North-Holland Publishing Co./American Elsevier Publishing Co., Amsterdam- London/New York, 1971.Search in Google Scholar

[32] MADDEN, J. J.-VERMEER, J.: Epicomplete Archimedean l-groups via a localic Yosida theorem, J. Pure Appl. Algebra 68 (1990), 243-252.10.1016/0022-4049(90)90147-ASearch in Google Scholar

[33] MOORE, E. H.: Introduction to a form of general analysis. In: New Haven Mathematical Colloquium, Yale Univ. Press, New Haven 1910, pp. 13-50.10.1090/coll/002/01Search in Google Scholar

[34] DE PAGTER, B.: f-algebras and Orthomorphisms. Thesis, Univ. of Leiden, 1981.Search in Google Scholar

[35] VEKSLER, A. I.: A new construction of Dedekind completion of vector lattices and of l-groups with division, Sib. Math. J. 10 (1969), 890-896.Search in Google Scholar

[36] YOSIDA, K.: On the representation of the vector lattice, Proc. Imp. Acad. Tokyo 18 (1942), 339-342 10.3792/pia/1195573861Search in Google Scholar