References
R. Balbes,Protective and injective distributive lattices, Pacific J. Math.21 (1967), 405–420.
R.Balbes and P.Dwinger,Distributive Lattices, University of Missouri Press, 1974.
R.Ball,Cauchy completions are homomorphic images of submodels of ultrapowers, Proceedings of the Conference on Convergence Structures, Department of Mathematics, Cameron University, Lawton, Oklahoma 73505.
R. Ball,Convergence and Cauchy structures on lattice ordered groups, Trans. Amer. Math. Soc.259 (1980), 357–392.
R.Ball,The distinguished completion of a lattice ordered group, Algebra Carbondale 1980, Lecture Notes in Mathematics 848, Springer-Verlag.
R.Ball,l-group completions from lattice completions, Ordered Algebraic Structures, Marcel Dekker, to appear.
R.Ball and G.Davis,The α-completion of a lattice ordered group, submitted to Czech. J. Math.
B. Banaschewski andG. Bruns,Categorical characterization of the MacNeille completion, Arch. Math.18 (1967), 369–377.
B. Banaschewski andG. Burns,Injective hulls in the category of distributive lattices, J. Reine Angew. Math.232 (1968), 102–109.
C. H. Cook andH. R. Fischer,Uniform convergence structures, Math. Annalen173 (1967), 290–306.
R. P. Dilworth,A decomposition theorem for partially ordered sets, Annals of Math.51 (1950), 161–166.
R. P. Dilworth andJ. E. McLaughlin,Distributivity in lattices. Duke Math. J.19 (1952), 683–694.
R. Frič andD. C. Kent,Completion functors for Cauchy spaces, Internat. J. Math, and Math. Sci.2 (1979), 589–604.
G.Grätzer,Universal Algebra, Van Nostrand, 1968.
T.Jech,Set Theory, Academic Press, 1978.
H. J. Keisler,Theory of models with generalized atomic formulas, J. Symbolic Logic25 (1960), 1–26.
D. C. Kent,On the order topology in a lattice, Illinois J. Math.10 (1966), 90–96.
D. C. Kent andG. D. Richardson,Regular completions of Cauchy spaces, Pacific J. Math.51 (1974), 483–490.
H. M. MacNeille,Partially ordered sets, Trans. Amer. Math. Soc.42 (1937), 416–460.
F. Papangelou,Some considerations on convergence in abelian lattice groups, Pacific J. Math.15 (1965), 1347–1364.
W. Peremans,Embedding of a distributive lattice into a Boolean algebra, Indag. Math.60 (1957), 73–81.
G. N. Raney,A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc.4 (1953), 518–522.
R. Sikorski,A theorem on extensions of homomorphisms, Ann. Soc. Pol. Math.21 (1948), 332–335.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ball, R.N. Distributive Cauchy lattices. Algebra Universalis 18, 134–174 (1984). https://doi.org/10.1007/BF01198525
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01198525