The variety of modular lattices is not generated by its finite members-Reference-Cited by-同舟云学术

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

Published:1979 Issue:0 Volume:255 Page:277-300
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Freese Ralph

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1979-255-00/S0002-9947-1979-0542881-0/S0002-9947-1979-0542881-0.pdf

Reference20 articles.

1. Equational classes of modular lattices;Baker, Kirby A.;Pacific J. Math.,1969

2. P. Crawley and R. P. Dilworth, Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs, N. J., 1973.

3. Component subsets of the free lattice on 𝑛 generators;Dean, Richard A.;Proc. Amer. Math. Soc.,1956

4. The arithmetical theory of Birkhoff lattices;Dilworth, R. P.;Duke Math. J.,1941

5. Planar sublattices of 𝐹𝑀(4);Freese, Ralph;Algebra Universalis,1976

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