Journal of the Australian Mathematical Society (Series A)

Table of Contents - Volume 47 - Issue01

Research Article

Pasting infinite lattices

E. Frieda1 and G. Grātzer

a1 Department of Mathematics, University of Manitoba Winnipeg, Manitoba, R3T 2N2, Canada

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, Axs2229B = S, Axs222AB = 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.

(Received September 29 1987)

1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision)

  • 06 B 05;
  • 06 B 20

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