About DML-CZ | FAQ | News | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Hager, Anthony W. ; Kimber, Chawne M. ; McGovern, Warren W.
Unique $a$-closure for some $\ell$-groups of rational valued functions. (English). Czechoslovak Mathematical Journal, vol. 55 (2005), issue 2, pp. 409-421
MSC: 06F20, 06F25, 20F60, 54C30, 54F65 | MR 2137147 | Zbl 1081.06020
Keywords:
archimedean lattice-ordered group; $a$-closure; rational-valued functions; zero-dimensional space
Summary:

References:
[1] M. Anderson and T. Feil: Lattice-Ordered Groups. Reidel, Dordrecht, 1989. MR 0937703
[2] E. Aron and A. Hager: Convex vector lattices and $\ell $-algebras. Topology Appl. 12 (1981), 1–10. MR 0600458
[3] A. Bigard, K. Keimel and S. Wolfenstein: Groupes et anneaux reticules. Springer-Verlag, Berlin-Heidelberg-New York, 1977. MR 0552653
[4] P. Conrad: Archimedean extensions of lattice-ordered groups. J. Indian Math. Soc. 30 (1966), 131–160. MR 0224519 | Zbl 0168.27702
[5] P. Conrad: Epi-archimedean groups. Czechoslovak. Math.  J. 24(99) (1974), 192–218. MR 0347701 | Zbl 0319.06009
[6] P. F. Conrad, M. R. Darnel and D. G. Nelson: Valuations of lattice-ordered groups. J. Algebra 192 (1997), 380–411. MR 1449966
[7] M. Darnel: Theory of Lattice-Ordered Groups. Pure and Applied Mathematics, Vol.  187. Dekker, New York, 1995. MR 1304052
[8] R. Engelking: General Topology. Heldermann, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[9] L. Gillman and M. Jerison: Rings of Continuous Functions. D.  Van Nostrand Publ., , 1960. MR 0116199
[10] A. Hager: Cozero fields. Confer. Sem. Mat. Univ. Bari. 175 (1980), 1–23. MR 0618363 | Zbl 0486.54019
[11] A. Hager: On inverse-closed subalgebras of  $C(X)$. Proc. London Math. Soc. 3 (1969), 233–257. MR 0244948 | Zbl 0169.54005
[12] A. Hager: Real-valued functions on Alexandroff (zero-set) spaces. Comm. Math. Univ. Carolin. 16 (1975), 755–769. MR 0394547 | Zbl 0312.54022
[13] A. Hager and C. Kimber: Some examples of hyperarchimedean lattice-ordered groups. Fund. Math. 182 (2004), 107–122. MR 2100062
[14] A. Hager, C. Kimber and W. McGovern: Least integer closed groups. Ordered Alg. Structure (2002), 245–260. MR 2083043
[15] A. W. Hager and J. Martinez: Singular archimedean lattice-ordered groups. Algebra Univ. 40 (1998), 119–147. MR 1651866
[16] A. Hager and L. Robertson: Representing and ringifying a Riesz space. Sympos. Math. 21 (1977), 411–431. MR 0482728
[17] M. Henriksen and D. Johnson: On the structure of a class of archimedean lattice-ordered algebras. Fund. Math. 50 (1961), 73–94. MR 0133698
[18] M. Henriksen, J. Isbell and D. Johnson: Residue class fields of lattice-ordered algebras. Fund. Math. 50 (1961), 107–117. MR 0133350
[19] C. Kimber and W. McGovern: Bounded away lattice-ordered groups. Manuscript, 1998.
[20] J. R. Porter and R. G. Woods: Extensions and Absolutes of Hausdorff Spaces. Springer-Verlag, , 1988. MR 0918341
[21] K. Yosida: On the representation of the vector lattice. Proc. Imp. Acad. Tokyo 18 (1942), 339–343. MR 0015378 | Zbl 0063.09070
Partner of
EuDML logo