Subdirectly irreducible members of products of lattice varieties

Grätzer, George; Kelly, David

doi:10.1090/S0002-9939-1988-0928965-4

Subdirectly irreducible members of products of lattice varieties
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by George Grätzer and David Kelly PDF

Proc. Amer. Math. Soc. 102 (1988), 483-489 Request permission

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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