The variety of modular lattices is not generated by its finite members

Freese, Ralph

doi:10.1090/S0002-9947-1979-0542881-0

The variety of modular lattices is not generated by its finite members
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by Ralph Freese

Trans. Amer. Math. Soc. 255 (1979), 277-300

DOI: https://doi.org/10.1090/S0002-9947-1979-0542881-0

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Abstract:

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.

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