J Austral Math Soc Ser A 47 pp1--21, 1989.

Pasting Infinite Lattices

E. Fried and G. Grätzer

Abstract

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 ÇB = S, A ÈB = 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. Jezek. Our main result is that the variety of all modular lattices and the variety of all distributive lattices are closed under pasting.

1980 AMS Subject Classification (1985 Revision): 06B05, 06B20

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Authors

E. Fried

G. Grätzer

Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada.