ar X iv : m at h / 05 01 43 6 v 1 [ m at h . G M ] 2 5 Ja n 20 05 TENSOR PRODUCTS OF SEMILATTICES WITH ZERO , REVISITED
نویسندگان
چکیده
Let A and B be lattices with zero. The classical tensor product, A ⊗ B, of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a lattice. We define a very natural condition: A ⊗ B is capped (that is, every element is a finite 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 ⊗ Conc B ∼ = Conc(A ⊗ B).
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