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Proceedings of the American Mathematical Society

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

 

 

Varieties with cofinal sets: examples and amalgamation


Authors: Peter Bruyns and Henry Rose
Journal: Proc. Amer. Math. Soc. 111 (1991), 833-840
MSC: Primary 08B10; Secondary 03C05, 03C20, 06B20, 08B25
DOI: https://doi.org/10.1090/S0002-9939-1991-1039528-7
MathSciNet review: 1039528
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Abstract: A variety $ \mathcal{V}$ has a cofinal set $ S \subset \mathcal{V}$ if any $ A \in \mathcal{V}$ is embeddable in a reduced product of members of $ S$. Amalgamation in and examples of such varieties are considered. Among other results, the following are proved: (i) every lattice is embeddable in an ultraproduct of finite partition lattices; (ii) if $ \mathcal{V}$ is a residually small, congruence distributive variety whose members all have one-element subalgebras, then the amalgamation class of $ \mathcal{V}$ is closed under finite products.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1039528-7
Article copyright: © Copyright 1991 American Mathematical Society