Varieties with cofinal sets: examples and amalgamation

Bruyns, Peter; Rose, Henry

doi:10.1090/S0002-9939-1991-1039528-7

Varieties with cofinal sets: examples and amalgamation
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by Peter Bruyns and Henry Rose PDF

Proc. Amer. Math. Soc. 111 (1991), 833-840 Request permission

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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