References
M. E. Adams andD. Kelly, Disjointness conditions in free products of lattices. Algebra Universalis7, 245–258 (1977).
I. Amemiya, Countable decomposability of vector lattices. J. Fac. Hokkaido Univ.19, 111–113 (1966).
K. A. Baker, Free vector lattices. Canad. J. Math.20, 58–66 (1968).
R.Balbes and P.Dwinger, Distributive lattices. Columbia 1974.
J. T. Baldwin, J. Bergman, A. M. W. Glass andW. Hodges, A combinatorial fact about free algebras. Algebra Universalis15, 145–152 (1982).
S. J. Bernau, Free abelian lattice groups. Math. Ann.180, 48–59 (1969).
G.Birkhoff, Lattice theory, 3rd ed. Amer. Math. Soc. Colloq. Publ.25, Providence 1967.
R. D. Bleier, Free ℓ-groups and vector lattices. J. Austral. Math. Soc.19, 337–342 (1975).
J. D. Franchello, Sublattices of free products of lattice ordered groups. Algebra Universalis8, 101–110 (1978).
G.Grätzer, Universal Algebra, 2nd. ed. New York-Heidelberg-Berlin 1979.
G. Grätzer andH. Lakser, The structure of pseudocomplemented distributive lattice. II. congruence extension and amalgamation. Trans. Amer. Math. Soc.156, 343–358 (1971).
W. C. Holland andE. Scrimger, Free products of lattice-ordered groups. Algebra Universalis2, 247–254 (1972).
R. B. Jensen, The fine structure of the constructible hierarchy. Ann. Math. Logic4, 229–308 (1972).
H.Lakser, Disjointness conditions in free products of distributive lattices: an application of Ramsay's theorem. Proc. Univ. of Houston Lattice Theory Conf., Houston 1973.
J. Martinez, Free products of abelian ℓ-groups. Czech. Math. J.23, 349–361 (1973).
H. Nakano, über das System aller stetigen Funktionen auf einen topologischen Raum. Proc. Imp. Acad. Tokyo17, 308–310 (1941).
W. B. Powell andC. Tsinakis, Free products in the class of abelian ℓ-groups. Pacific J. Math.104, 429–442 (1983).
W. B. Powell andC. Tsinakis, The distributive lattice free product as a sublattice of the abelian ℓ-group free product. J. Austral. Math. Soc.34, 92–100 (1983).
M. H. Stone, Boundedness properties of function lattices. Canad. J. Math.1, 176–186 (1949).
E. C. Weinberg, Free lattice-ordered groups. Math. Ann.151, 187–199 (1963).
E. C. Weinberg, Free lattice-ordered groups II. Math. Ann.159, 217–222 (1965).
Author information
Authors and Affiliations
Additional information
Research supported in part by an A. & S. Research Grant from Oklahoma State University.
Research supported by the Vanderbilt University Research Council.
Rights and permissions
About this article
Cite this article
Powell, W.B., Tsinakis, C. Disjointness conditions for free products of ℓ-groups. Arch. Math 46, 491–498 (1986). https://doi.org/10.1007/BF01195016
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01195016