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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: Ralph Freese
Journal: Trans. Amer. Math. Soc. 255 (1979), 277-300
MSC: Primary 06C05; Secondary 06C20
DOI: https://doi.org/10.1090/S0002-9947-1979-0542881-0
MathSciNet review: 542881
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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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DOI: https://doi.org/10.1090/S0002-9947-1979-0542881-0
Article copyright: © Copyright 1979 American Mathematical Society