Amalgamation in small varieties of lattices

AbstractA property used by G. Grätzer and H. Lakser to describe the amalgamation class of a finitely generated variety of pseudo-complemented distributive lattices, and a property used by C. Bergman in his investigations of the amalgamation classes of varieties that are finitely generated, congruence distributive and semi-simple, are here applied to arbitrary finitely generated, con- gruence distributive varieties. The Grätzer-Lakser property is shown to characterize the amalgamation class of a finitely generated variety V of lattices. For finite lattices, this gives an effective test for membership in the amalgamation class of V. For V=N, the variety generated by the pentagon, an even simpler test is found