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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  • Fuzzy Sets Syst.
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TLDR
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