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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Universality of small lattice varieties


Authors: V. Koubek and J. Sichler
Journal: Proc. Amer. Math. Soc. 91 (1984), 19-24
MSC: Primary 06B20; Secondary 08B05, 18B15
MathSciNet review: 735556
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Abstract: There exists a finitely generated lattice variety $ S$ such that the class of all nonconstant homomorphisms between members of $ S$ contains a universal category as a full subcategory. In particular, every monoid $ M$ is isomorphic to the monoid of all nonconstant endomorphisms of a lattice from $ S$, and $ S$ contains arbitrarily large lattices representing $ M$. The category of all $ (0,1)$-homomorphisms of lattices in $ S$ is also shown to be universal.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735556-3
Article copyright: © Copyright 1984 American Mathematical Society