Tensor products and transferability of semilattices
  In general, the tensor product, $A\otimes B$, of the lattices A and B with zero is not a lattice (it is only a join-semilattice with zero). If $A \otimes B$ is a capped tensor product, then $A \otimes B$ is a lattice (the converse is not known). In this paper, we investigate lattices A with zero enjoying the property that $A \otimes B$ is a capped tensor product, for every lattice B with zero; we shall call such lattices amenable. The &#64257;rst author introduced in 1966 the concept of a sharply transferable lattice. In 1972, H. Gaskill [5] de&#64257;ned, similarly, sharply transferable semilattices, and characterized them by a very e&#64256;ective condition (T). We prove that a &#64257;nite lattice A is amenable iff it is sharply transferable as a join-semilattice. For a general lattice A with zero, we obtain the result: A is amenable iff A is locally &#64257;nite and every &#64257;nite sublattice of A is transferable as a join-semilattice. This yields, for example, that a &#64257;nite lattice A is amenable iff $A\otimes F(3)$ is a lattice iff A satis&#64257;es (T), with respect to $\jj$. In particular, $M3 \otimes F(3)$ is not a lattice. This solves a problem raised by R. W. Quackenbush in 1985 whether the tensor product of lattices with zero is always a lattice. 
George Gr\"atzer, Friedrich Wehrung (LMNO)