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Pasting infinite lattices

Part of: Lattices

Published online by Cambridge University Press:  09 April 2009

E. Fried  and
G. Grātzer
E. Fried
Affiliation:
Department of Mathematics, University of ManitobaWinnipeg, Manitoba, R3T 2N2, Canada
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Abstract

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In an earlier paper, we investigated for finite lattices a concept introduced by A. Slavik: Let A, B, and S be sublattices of the lattice L, A∩B = S, A∪B = L. Then L pastes A and B together over S, if every amalgamation of A and B over S contains L as a sublattice. In this paper we extend this investigation to infinite lattices. We give several characterizations of pasting; one of them directly generalizes to the infinite case the characterization theorem of A. Day and J. Ježk. Our main result is that the variety of all modular lattices and the variety of all distributive lattices are closed under pasting.

MSC classification

Secondary: 06B05: Structure theory 06B20: Varieties of lattices

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 1 , August 1989 , pp. 1 - 21
Copyright
Copyright © Australian Mathematical Society 1989

References

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