Tensor Products and Transferability of Semilattices
نویسندگان
چکیده
منابع مشابه
Tensor 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...
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If M is a finite complemented modular lattice with n atoms and D is a bounded distributive lattice, then the Priestley power M [D] is shown to be isomorphic to the poset of normal elements of Dn, thus solving a problem of E. T. Schmidt from 1974. It is shown that there exist a finite modular lattice A not having M4 as a sublattice and a finite modular lattice B such that A⊗B is not semimodular,...
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The tensor product of semilattices has been studied in [2], [3] and [5]. A survey of this work is given in [4]. Although a number of problems were settled completely in these papers, the question of the associativity of the tensor product was only partially answered. In the present paper we give a complete solution to this problem. For terminology and basic results of lattice theory and univers...
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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...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1999
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1999-034-6