Modular and distributive semilattices
نویسندگان
چکیده
منابع مشابه
Modular and Distributive Semilattices
A modular semilattice is a semilattice S in which w > a A ft implies that there exist i,jeS such that x > a. y > b and x A y = x A w. This is equivalent to modularity in a lattice and in the semilattice of ideals of the semilattice, and the condition implies the Kurosh-Ore replacement property for irreducible elements in a semilattice. The main results provide extensions of the classical charac...
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We prove that for every distributive 〈∨, 0〉-semilattice S, there are a meet-semilattice P with zero and a map μ : P × P → S such that μ(x, z) ≤ μ(x, y)∨μ(y, z) and x ≤ y implies that μ(x, y) = 0, for all x, y, z ∈ P , together with the following conditions: (P1) μ(v, u) = 0 implies that u = v, for all u ≤ v in P . (P2) For all u ≤ v in P and all a,b ∈ S, if μ(v, u) ≤ a ∨ b, then there are a pos...
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We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neu-mann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these diierent topics.
متن کاملThe median function on distributive semilattices
A median of a k-tuple =(x1; : : : ; xk) of elements of a 0nite metric space (X; d) is an element x for which ∑k i=1 d(x; xi) is minimum. The function m with domain the set of all k-tuples with k ¿ 0 and de0ned by m( ) = {x: x is a median of } is called the median function on X . Continuing with the program of characterizing m on various metric spaces, this paper presents a characterization of t...
متن کاملPriestley Style Duality for Distributive Meet-semilattices
We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms....
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1975
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1975-0351935-x