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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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