Tensorial decomposition of concept lattices. (English) Zbl 0583.06007

The author continues his investigation on concept lattices, a field of promising applications. He shows that the tensor product of continuous lattices reflects the product of contexts. In the third part, he takes a closer look at the tensor product and in the fourth part, the subdirect decomposition of the tensor product is investigated. In the last part, he shows how tensor products can be used in finding a scale for contexts.
Reviewer: E.Fried


06B05 Structure theory of lattices
06B23 Complete lattices, completions
06B30 Topological lattices
Full Text: DOI


[1] B. Banaschewski and E. Nelson (1976) Tensor products and bimorphisms, Canad. Math. Bull. 19, 385-402. · Zbl 0392.18003
[2] H.-J. Bandelt (1980) The tensor product of continuous lattices, Math. Z. 172, 89-96. · Zbl 0424.06003
[3] H.-J. Bandelt (1980) Coproducts of bounded (?, ?)-distributive lattices, Alg. Universalis 17, 92-100. · Zbl 0524.06018
[4] M. Barbut and B. Monjardet (1970) Ordre et classification, alg?bre et combinatoire, II, Hachette, Paris. · Zbl 0267.06001
[5] G. Gr?tzer, H. Lakser, and R. Quackenbush (1981) The structure of tensor products of semilattices with zero, Trans. Amer. Math. Soc. 267, 503-515. · Zbl 0478.06003
[6] G. Kalmbach (1976) Extension of topological homology theories to partially ordered sets, J. reine angew. Math. 280, 134-156. · Zbl 0322.06004
[7] D. G. Mowat (1968) A Galois problem for mappings, PhD Thesis, Univ. of Waterloo. · Zbl 0285.06002
[8] E. Nelson (1976) Galois connections as left adjoint maps, Comment. Math. Univ. Carolinae 17, 523-541. · Zbl 0344.06003
[9] G. N. Raney (1952) Completely distributive complete lattices, Proc. Amer. Math. Soc. 3, 677-680. · Zbl 0049.30304
[10] G. N. Raney (1960) Tight Galois connections and complete distributivity, Trans. Amer. Math. Soc. 97, 418-426. · Zbl 0098.02703
[11] Z. Shmuely (1974) The structure of Galois connections, Pac. J. Math. 54, 209-225. · Zbl 0275.06003
[12] Z. Shmuely (1979) The tensor product of distributive lattices, Alg. Universalis 9, 281-296. · Zbl 0426.06003
[13] A. G. Waterman (1966) Colloquium lecture at McMaster University.
[14] R. Wille (1982) Restructuring lattice theory: an approach based on hierarchies of concepts, in: Ordered Sets (ed I. Rival), Reidel, Dordrecht, Boston, pp. 445-470.
[15] R. Wille (1983) Subdirect decomposition of concept lattices, Alg. Universalis 17, 275-287. · Zbl 0539.06006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.