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.)
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