Abstract
This chapter discusses a duality for the lattice variety generated by M3. Many dualities and representation theorems have developed from a representation of the finite or finitely generated algebras in the variety in question. Often the aim was to find a good description of free algebras to solve certain decision problems such as the word problem. Such a representation for finite lattices was given by R. Wille, which was an excellent tool for determing the sizes of free lattices in the variety M3 generated by ▪. K. Keimel and G. Gierz extended Wille's notion of a GERÜST to infinite lattices, thereby, obtaining a representation theorem for the variety of all lattices. Unfortunately, this representation is not constructive in any sense and the only way to construct the Gerüst of some lattice is via the knowledge of all its subdirectly irreducible quotients. The chapter presents a different approach to dualities that works particularly well for finite algebras with an underlying lattice structure.
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