A non-capped tensor product of lattices
نویسندگان
چکیده
In the lattice theory the tensor product A⊗B is naturally defined on (0,∨)−semilattices. In general, when restricted to lattices this construction will not yield a lattice. However, if the tensor product A ⊗ B is capped, then A⊗B is a lattice. It is stated as an open problem in [4] whether the converse is true. In the present paper we prove that it is not so, that is, there are bounded lattices A and B such that A⊗B 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.
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