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Proceedings of the American Mathematical Society

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

 

 

Subdirectly irreducible members of products of lattice varieties


Authors: George Grätzer and David Kelly
Journal: Proc. Amer. Math. Soc. 102 (1988), 483-489
MSC: Primary 06B20
DOI: https://doi.org/10.1090/S0002-9939-1988-0928965-4
MathSciNet review: 928965
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Abstract: In this paper we prove:

Theorem. Let $ \mathbf{V}$ and $ \mathbf{W}$ be nontrivial lattice varieties. If $ L \in \mathbf{V} \circ \mathbf{W}$, then there is a subdirectly irreducible $ S \in \mathbf{V} \circ \mathbf{W}$ containing $ L$ as a sublattice. Moreover, if $ L$ is finite, $ S$ can also be chosen to be finite.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0928965-4
Article copyright: © Copyright 1988 American Mathematical Society