A non-capped tensor product of lattices

Bogdan Chornomaz (1)

1 NASU - National Academy of Sciences of Ukraine

In the lattice theory the tensor product A B is naturally de ned on join-semilattices with zero. In general, when restricted to lattices this construction will not yield a lattice. However, if the tensor product of A and B is capped, then their tensor product is a lattice. In this paper we prove that it the converse does not hold in general, that is, there are bounded lattices A and B such that their tensor product is not capped, but is a lattice. Furthermore, A has length three and is generated by a nine-element set of atoms, while B is the dual lattice of A.

Mots clés: lattice; tensor product; capped tensor product

Domaines: Mathématiques générales [math.GM]

Bogdan Chornomaz. A non-capped tensor product of lattices. 2013. ⟨hal-00909356⟩