Coproducts of distributive lattice-based algebras
نویسندگان
چکیده
منابع مشابه
Coproducts of Distributive Lattice based Algebras
The analysis of coproducts in varieties of algebras has generally been variety-specific, relying on tools tailored to particular classes of algebras. A recurring theme, however, is the use of a categorical duality. Among the dualities and topological representations in the literature, natural dualities are particularly well behaved with respect to coproduct. Since (multisorted) natural dualitie...
متن کاملCoproducts of Bounded Distributive Lattices
Let LM denote the coproduct of the bounded distributive lattices L and M. At the 1981 Bann Conference on Ordered Sets, the following question was posed: What is the largest class L of nite distributive lattices such that, for every non-trivial Boolean lattice B and every L 2 L, B L = B L 0 implies L = L 0 ? In this note, the problem is solved.
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Let L ∗ M denote the coproduct of the bounded distributive lattices L and M . At the 1981 Banff Conference on Ordered Sets, the following question was posed: What is the largest class L of finite distributive lattices such that, for every non-trivial Boolean lattice B and every L ∈ L, B ∗ L = B ∗ L′ implies L = L′? In this note, the problem is solved.
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While the study of quantale-like structures goes back up to the 1930’s (notwithstanding that the term itself was introduced in [2] in connection with certain aspects of C∗-algebras), there has recently been much interest in quantales in a variety of contexts. The most important connection probably is with Girard’s linear logic. In particular, one can enunciate the following slogan: Quantales ar...
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Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2014
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-014-0302-3