Tensor products of semilattices with zero, revisited
  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 de&#64257;ne a very natural condition: $A \otimes B$ is capped (that is, every element is a &#64257;nite 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 holds for any capped tensor product: $Conc A\otimes Conc B \cong Conc(A \otimes B)$. This generalizes from &#64257;nite lattices to arbitrary lattices the main result of a joint paper by the &#64257;rst author, H. Lakser, and R. W. Quackenbush. 
George Gr\"atzer, Friedrich Wehrung (LMNO)