Geodesic
Free Decompositions of a Lattice
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 276-285

Voir la notice de l'article provenant de la source Cambridge University Press

Two basic questions have been raised for free products of lattices:1. Do any two free products have a common refinement?2. Can every lattice be decomposed into a free product of freely indecomposable lattices?Both questions have been around for some time and attempts at solving them were made especially after the Structure Theorem for Free Products was discovered (see G. Grâtzer, H. Lasker, and C. R. Piatt [3]). Partial answer to question one was supplied in A. Kostinsky [7].In this paper we answer both questions. Our basic observation is that the proper framework for these results is the theory of free K-products, that is, free products in an arbitrary equational class K of lattices. 
Grätzer, G.; Sichler, J. Free Decompositions of a Lattice. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 276-285. doi: 10.4153/CJM-1975-034-5
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