The amalgamation property in equational classes of modular lattices
George Grätzer, Bjàrni Jónsson, H. Lakser · Pacific Journal of Mathematics · 1973
It is known that the class of all distributive lattices satisfies the Amalgamation Property.It will be shown that this is the only nontrivial equational class of modular lattices for which the Amalgamation Property holds.A second theorem gives further information about the Amalgamation Class of the class of all modular lattices, and of certain other equational classes.1* Introduction* A class K of algebras (or in general, structures) is said to have the Amalgamation Property if for A, B o , B λ in K and for embeddings f { : A-+B { , i -0, 1, there exist a C in K and embeddings g { : B { -> C, i = 1, 2, such that f o g o -f 1 g 1 (see Figure 1).