# Tensor products of semilattices with zero, revisited

@article{Gratzer2000TensorPO, title={Tensor products of semilattices with zero, revisited}, author={Georg Gratzer and Friedrich Wehrung}, journal={Journal of Pure and Applied Algebra}, year={2000}, volume={147}, pages={273-301} }

Let A and B be lattices with zero. The classical tensor product, $A\otimes B$, of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a lattice. We deﬁne a very natural condition: $A \otimes B$ is capped (that is, every element is a ﬁnite union of pure tensors) under which the tensor product is always a lattice. Let Conc L denote the join-semilattice with zero of compact congruences of a lattice L. Our main result is that the following isomorphism… Expand

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