. 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).
منابع مشابه
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
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 c...
متن کاملJa n 20 05 A NEW LATTICE CONSTRUCTION : THE BOX PRODUCT
In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism Conc(A ⊗ B) ∼ = Conc A ⊗ Conc B, holds, provided that the tensor product satisfies a very natural condition (of being capped) implying that A ⊗ B is a lattice. In general, A ⊗ B is not a lattice; for instance, we proved that M 3 ⊗ F(3) is not a lattice. In this paper, we introduce a new lattice const...
متن کاملTensor Products and Transferability of Semilattices
In general, the tensor product, A ⊗ B, of the lattices A and B with zero is not a lattice (it is only a join-semilattice with zero). If A ⊗ B is a capped tensor product, then A ⊗ B is a lattice (the converse is not known). In this paper, we investigate lattices A with zero enjoying the property that A ⊗ B is a capped tensor product, for every lattice B with zero; we shall call such lattices ame...
متن کاملIrreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$
We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$. We specialize the indeterminates used in defining these representations to non zero complex numbers. We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$. We then determine necessary and sufficient conditions that guarantee the irreducibility of th...
متن کاملar X iv : m at h / 05 01 45 4 v 1 [ m at h . A G ] 2 5 Ja n 20 05 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES
We calculate the dimension of the locus of elliptic surfaces over P 1 with a section and a given Picard number, in the corresponding moduli space.
متن کامل