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Permutability of Semilattice Congruences on Lattices

Published online by Cambridge University Press:  20 November 2018

Tsuyoshi Fujiwara
Tsuyoshi Fujiwara*
Affiliation:
University of Osaka Prefecture, Japan
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Many authors have studied lattice congruences on lattices, but it seems that there are few studies concerning semilattice congruences on lattices. However, it seems that the semilattice congruences on lattices are closely connected with their structure. In this paper, we shall study the characterizations of modular, distributive, and relatively complemented lattices by the permutability of semilattice congruences.

We can obtain the dual statements of the following discussion, but we shall not write them as a rule to avoid double descriptions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 370 - 375
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Dilworth, R. P., The structure of relatively complemented lattices, Ann. Math., 51 (1950), 348–359.Google Scholar