Pasting infinite lattices
Ervin Fried, George Grätzer · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1989
Abstract In 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.