The Variety of Modular Lattices is Not Generated by its Finite Members

Ralph Freese
1979 Transactions of the American Mathematical Society  
This paper proves the result of the title. It shows that there is a five-variable lattice identity which holds in all finite modular lattices but not in all modular lattices. It is also shown that every free distributive lattice can be embedded into a free modular lattice. An example showing that modular lattice epimorphisms need not be onto is given.
doi:10.2307/1998176 fatcat:uusavipqajfpdfsizhwudif5si