Abstract
The notions of gluing, tolerance relations, and Mal'cev products of varieties have been used by various authors to investigate varieties of lattices. In this paper the authors introduce a general framework for all these concepts and apply it to varieties of modular and Arguesian lattices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. J. Bandelt (1981) Tolerance relations on lattices, Bull. Austral. Math. Soc. 23 367–381.
G. Czédli (1982) Factor lattices by tolerances, Acta Sci. Math. 44 35–42.
A. Day, and B. Jónsson (1986) A structural characterization of non-Arguesian modular lattices, Order 2, 335–350.
R. Dilworth and R. Freese (1976) Generators for lattice varieties, Alg. Univ. 6, 263–267.
R. Freese (1979) Projective geometries as projective modular lattices, Trans. Amer. Math. Soc. 251, 329–342.
R. Freese, A decomposition theorem for modular lattices cotaining an n-diamond, Acta. Sci. Math. (to appear).
E. Graczynska (1977) On the sums of double systems of lattices, Coll. Math. Soc. J. Bolyai 17, 161–166.
E. Graczynska and G. Grätzer (1980) On double systems of lattices, Demonstratio Math. 13, 743–747.
G. Grätzer and D. Kelly (1980) A survey of products of lattice varieties, Coll. Math. Soc. J. Bolyai 33, 457–469.
G. Grätzer and E. Fried, Notes on tolerance relations of lattices, manuscript.
T. Harrison (1985) A problem concerning the lattice varietal products, Thesis, University of Hawaii, Honolulu.
Ch. Herrmann (19773) S-Verklebte Summen von Verbänden, Math. Z. 130, 255–274.
Ch. Herrmann (1973) Quasiplanare Verbände, Arch. Math. 24, 240–246.
Ch. Herrmann (1976) On modular lattices generated by two complemented pairs, Houston J. Math. 2, 512–523.
Ch. Herrmann (1983) On the word problem for the modular lattice with four free generators, Math. Ann. 265, 513–527.
Ch. Herrmann and A. Huhn (1975) Lattices of normal subgroups generated by frames, Coll. Math. Soc. J. Bolvai, 14, 97–136.
A. Huhn (1972) Schwach distributive Verbände I, Acta Sci. Math. 33, 297–305.
B. Jónsson (1959) Arguesian lattices of dimension n≤4, Math. Scand. 7, 133–145.
R. McKenzie (1972) Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc. 174, 1–43.
R. McKenzie and D. Hobby, The structure of finite algebras (tame congruence theory), Contemporary Mathematics, Amer. Math. Soc., Providence, RI.
R. Wille (1973) On modular lattices generated by finite chains, Alg. Univ. 3, 131–138.
R. Wille (1985) Complete tolerance relations of concept lattices, in Contributions to General Algebra III, (G. Eigenthaler ed.) Vienna, pp. 397–415.
R. Wille (1977) Eine Charakterisierung endlicher, ordnungspolynomvollständiger Verbände, Arch. Math. 28, 557–560.
Author information
Authors and Affiliations
Additional information
Communicated by R. P. Dilworth
Rights and permissions
About this article
Cite this article
Day, A., Herrmann, C. Gluings of modular lattices. Order 5, 85–101 (1988). https://doi.org/10.1007/BF00143900
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00143900