Hager, Anthony W.; Martinez, Jorge
Functorial approximation to the lateral completion in archimedean lattice-ordered groups with weak unit
Rendiconti del Seminario Matematico della Università di Padova, Tome 105 (2001) , p. 87-110
Zbl 1095.18500 | MR 1834983
URL stable : http://www.numdam.org/item?id=RSMUP_2001__105__87_0

Bibliographie

[AF] M. Anderson - T. Feil, Lattice-ordered groups, Reidel, Dordrecht (1988). MR 937703 | Zbl 0636.06008

[AH] E.R. Aron - A.W. Hager, Convex vector lattices and l-algebras, Topology and Appl., 12 (1981), pp. 1-10. MR 600458 | Zbl 0458.06012

[B] B. Banaschewski, Maximal rings of quotients of semi-simple commutative rings, Archiv Math., XVI (1965), pp. 414-420. MR 199214 | Zbl 0135.07901

[BH1] R.N. Ball - A.W. Hager, Epicomplete Archimedean l-groups, Trans. Amer. Math. Soc., 32 (1990), pp. 459-478. MR 943603 | Zbl 0713.06006

[BH2] R.N. Ball - A.W. Hager, Epicompletion of Archimedean l-group and vector lattices with weak unit, J. Austral. Math. Soc., 48 (1990), pp. 25-56. MR 1026835 | Zbl 0696.06011

[BH3] R.N. Ball - A.W. Hager, Applications of spaces with filters to archimedean l-groups with weak unit, in: Ordered Algebraic Structures J. Martinez, Editor, Kluwer Academic Publishers, Dordrecht 1989, pp. 99-112. MR 1094829 | Zbl 0712.06011

[BH4] R.N. Ball - A.W. Hager, Algebraic extensions of an archimedean lattice-ordered group I, Jour. Pure and Appl. Alg., 85 (1993), pp. 1-20. MR 1207064 | Zbl 0776.06014

[BH5] R.N. Ball - A.W. Hager, Algebraic extensions of an archimedean lattice-ordered group II, Jour. Pure and Appl. Alg., 138 (1999), pp. 197-204. MR 1691480 | Zbl 0952.06023

[BHM] R.N. Ball - A.W. Hager - A.J. Macula, An a-disconnected space has no proper monic preimage, Top. and Its. Appl., 37 (1990), pp. 141-151. MR 1080348 | Zbl 0734.54005

[BKW] A. Bigard - K. Keimel - S. Wolfenstein, Groupes et anneaux reticuLes, Springer Lecture Notes 608, Berlin-Heidelberg- New York (1977). MR 552653 | Zbl 0384.06022

[Cl] P.F. Conrad, The lateral completion of a lattice-ordered group, Proc. London Math. Soc., 19 (1969), pp. 444-480. MR 244125 | Zbl 0182.04803

[C2] P.F. Conrad, The essential closure of an archimedean lattice-ordered group, Duke Math. Jour., 38 (1971), pp. 151-169. MR 277457 | Zbl 0216.03104

[DHH] F. Dashiell - A.W. Hager - M. Henriksen, Order-Cauchy completions of rings and vector lattices of continuous functions, Canad. J. Math., 32 (1980), pp. 657-685. MR 586984 | Zbl 0462.54009

[E] R. Engelking, General Topology, Sigma Series in Pure Math., 6 Heldermann, Berlin (1989). MR 1039321 | Zbl 0684.54001

[FGL] N.J. Fine - L. Gillman - J. Lambek, Rings of quotients of rings of functions, McGill University Press, Montreal (1965). MR 200747 | Zbl 0143.35704

[G] A. Gleason, Projective topological spaces, Illinois J. Math., 2 (1958), pp. 482-489. MR 121775 | Zbl 0083.17401

[GJ] L. Gillman - M. Jerison, Rings of continuous functions, Van No-strand Co., Princeton 1960, reprinted as Springer Verlag Graduate Texts 43, Berlin-Heidelberg -New York (1976). MR 116199 | Zbl 0327.46040

[HI] A.W. Hager, Perfect maps and epireflective hulls, Canad. J. Math., 27 (1975), pp. 11-24. MR 365499 | Zbl 0313.54013

[H2] A.W. Hager, Algebraic closures of L-groups of continuous functions, C. Aull, ed., Rings Continuous Functions, Lecture Notes Pure and Applied Mathematics, 95 (Dekker, New York, 1985), pp. 164-194. MR 789270 | Zbl 0616.06017

[H3] A.W. Hager, MinimaL covers of Topological Spaces, Ann. NY Acad. Sci., Papers on Gen. Topol. and Rel. Cat. Th. and Top. Alg., 552 (1989), pp. 44-59. MR 1020773 | Zbl 0881.54025

[HK] A.W. Hager - A. Kizanis, Certain extensions and factorizations of a-complete homomorphisms in archimedean lattice-ordered groups, J. Austral. Math Soc., 62 (1997), pp. 239-258. MR 1433212 | Zbl 0883.06012

[HMad] A.W. Hager - J.J. Madden, Essential reflections versus minimaL embeddings, J. Pure and Appl. Algebra, 37 (1985), pp. 27-32. MR 794790 | Zbl 0596.18001

[HR1] A.W. Hager - L.C. Robertson, Representing and ringifying a Riesz space, Symposia Mathematica, 21 (1977), pp. 411-431. MR 482728 | Zbl 0382.06018

[HR2] A.W. Hager - L.C. Robertson, On the embedding into a ring of an archimedean l-group, Canad. J. Math., 31 (1979), pp. 1-8. MR 518700 | Zbl 0406.06007

[HM1] A.W. Hager - J. Martinez, Functorial rings of quotients I, Proc. Conf. Ord. Alg. Struct.. Gainesville (1991), W.C. Holland and J. Martinez, Eds. Kluwer, Dordrecht, The Netherlands, 1993, pp. 133-157. MR 1247303 | Zbl 0792.06017

[HM2] A.W. Hager - J. Martinez, Functorial rings of quotients 2, The ring of hyper-fractions, Forum Math., 6 (1994), pp. 597-616. MR 1295154 | Zbl 0804.18002

[HM3] A.W. Hager - J. Martinez, Maximum monoref Lections, Appl. Cat. Str., 2 (1994), pp. 315-329. MR 1300719 | Zbl 0809.18003

[HM4] A.W. Hager - J. Martinez, Pushout-invariant extensions and monoreflections, Jour. Pure and Aplied Alg., 129 (1998), pp. 263-295. MR 1631253 | Zbl 0935.18002

[HM5] A.W. Hager - J. Martinez, a-projectable and LateraLLy a-complete archimedean lattice-ordered groups, Proc. Conf. in Memory of T. Retta, Temple, PA/ Addis-Ababa 1995; S. Berhanu, Ed.; Ethiopian Jour. Sci. (1996), pp. 73-84.

[HM6] A.W. Hager -J. Martinez, The laterally σ-complete reflection of an archimedean l-group, in Proc. Conf. Ordered Alg. Structures (Curagao, 1995), W.C. Holland and J. Martinez, Eds., Kluwer, Dordrecht, The Netherlands, 1997, pp. 217-236. Zbl 0874.06013

[HM7] A.W. Hager - J. Martinez, Hulls for various kinds of a-completeness in archimedean lattice-ordered groups, Order, 16 (1999), pp. 89-103. MR 1740743 | Zbl 0953.06017

[HM8] A.W. Hager - J. Martinez, Maximum monoreflections and essential extensions, Appl. Cat. Str., to appear. MR 1865615 | Zbl 1016.18002

[HM9] A.W. Hager - J. Martinez, More on the laterally σ-complete reflection of an archimedean lattice-ordered group, Order, 15 (1999), pp. 247-260. Zbl 0936.06016

[HM ∞] A.W. Hager - J. Martinez, Functorial rings of quotients 3: The maximum for archimedean f-rings, Jour. Pure and Appl. Alg., to appear. Zbl 0993.06016

[HI] M. Henriksen - J. Isbell, Some properties of compactifications, Duke Math J., 25 (1958), pp. 83-105. MR 96196 | Zbl 0081.38604

[HJ] M. Henriksen - D.G. Johnson, On the structure of a class of archimedean lattice-ordered algebras, Fund. Math., 50 (1961), pp. 73-94. MR 133698 | Zbl 0099.10101

[HS] H. Herrlich - G.E. Strecker, Category Theory, 2nd. Ed., Sigma Ser. Pure Math. I, Heldermann Verlag, Berlin (1970). MR 571016 | Zbl 0437.18001

[J] D.G. Johnson, Rings of quotients of ϕ-algebras, Proc. J. Math., 36 (1971), pp. 693-699. Zbl 0192.48301

[K] A. Kizanis, Epicompletions of archimedean lattice-ordered groups, Thesis, Wesleyan Univ. (1991).

[PW] J.R. Porter - R.G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer-Verlag (1988). MR 918341 | Zbl 0652.54016

[R] W. Rudin, Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc., 8 (1957), pp. 39-42. MR 85475 | Zbl 0077.31103

[S] Z. Semadeni, Banach Spaces of Continuous Functions, Vol. I, PWN, Warsaw (1971). MR 296671 | Zbl 0225.46030

[T] Z. Tzeng, Extended real valued functions and the projective resolution of a compact Hausdorff space, Thesis, Wesleyan Univ. (1970).

[V] A. Veksler, P-sets in topological spaces, Soviet Math Dokl., 11 (1970), pp. 953-956 MR 279759 | Zbl 0214.49704

[VG] A. Veksler -V. Geiler, Order and disjoint completeness of linear partially ordered spaces, Plenum Translation (1972) of Sibr. Math. Z., 13 (1972), pp. 43-51. MR 296654 | Zbl 0333.06009