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Generalized Boolean lattices

Published online by Cambridge University Press:  09 April 2009

Richard D. Byrd ,
Roberto A. Mena  and
Linda A. Troy
Richard D. Byrd
Affiliation:
University of Houston, U.S.A.
Roberto A. Mena
Affiliation:
University of Houston, U.S.A.
Linda A. Troy
Affiliation:
University of Wyoming, U.S.A.
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Hashimoto (1952; Theorems 8.3 and 8.5) proved the following theorems: Theorem A. If L, is a distributive lattice, then there exists a generalized Boolean alegbra Lr and an isomorphism from the lattice of all congruence relations of L onto the lattice of all congruence relations of Lr.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 2 , March 1975 , pp. 225 - 237
Copyright
Copyright © Australian Mathematical Society 1975

References

Grätzer, G. (1971), Lattice Theory, (W. H. Freeman and Company, San Francisco, 1971).Google Scholar
Grätzer, G. and Schmidt, E. T. (1958), ‘On the generalized Boolean algebra generated by a distributive lattice’, Indag. Math. 20, 54–553.Google Scholar
Hashimoto, J. (1953), ‘Ideal theory for lattices’, Math. Japan. 2, 149–186.Google Scholar