Abstract. In 1970, R. Freese proved that the variety ${\bf M}^4$ generated by modular lattices of width at most $4$ has a finite basis. As an application, he obtained a complete description of all subdirectly irreducible members of this variety. We obtain an intuitive description of how congruences generated by a prime interval spread in a modular lattice of width at most $4$, and apply the result to reprove Freese's description of subdirectly irreducible lattices of width at most $4$.

AMS Subject Classification (1991): 06C05; 06B20

Keyword(s): lattice, modular, width, subdirectly irreducible, snake, weakly atomic

Received July 11, 2006, and in revised form November 24, 2006. (Registered under 5951/2009.)