Abstract
AbstractIn an earlier paper, we investigated for finite lattices a concept introduced by A. Slavik: LetA, B,andSbe sublattices of the latticeL,A∩B=S,A∪B=L. ThenL pastes AandBtogether overS, if every amalgamation ofAandBoverScontainsLas 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.
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More From: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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