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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
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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Article copyright: © Copyright 1988 American Mathematical Society

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