The Semilattice Tensor Product of Distributive Lattices
Grant A. Fraser · Transactions of the American Mathematical Society · 1976
We define the tensor product $A \otimes B$ for arbitrary semilattices A and B. The construction is analogous to one used in ring theory (see [4], [7], [8]) and different from one studied by A. Waterman [12], D. Mowat [9], and Z. Shmuely [10]. We show that the semilattice $A \otimes B$ is a distributive lattice whenever A and B are distributive lattices, and we investigate the relationship between the Stone space of $A \otimes B$ and the Stone spaces of the factors A and B. We conclude with some results concerning tensor products that are projective in the category of distributive lattices.