The tensor product of distributive lattices
نویسندگان
چکیده
منابع مشابه
The Semilattice Tensor Product of Distributive Lattices
We define the tensor product A ® S for arbitrary semilattices A and B. The construction is analogous to one used in ring theory (see 14], [7], [8]) and different from one studied by A. Waterman [12], D. Mowat [9], and Z. Shmuely [10]. We show that the semilattice A <3 B is a distributive lattice whenever A and B are distributive lattices, and we investigate the relationship between the Stone sp...
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1. Introduction. A typical result of this paper is the following. Let Lt, i e I be distributive lattices satisfying the countable chain condition. Then the free product L of these lattices also satisfies the countable chain condition. To be able to state the general result we need some notations. Let trt be an infinite cardinal. A poset (partially ordered set) P is said to satisfy the m-chain c...
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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...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1976
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500010622