Results 221 to 230 of about 3,104 (252)
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On Lattice Embeddings for Partially Ordered Sets
Canadian Journal of Mathematics, 1954Let P be a set partially ordered by a (reflexive, antisymmetric, and transitive) binary relation ≺. Let be the family of all subsets K of P having the property that x ∈ P and y ∈ K and y ≺ x imply x ∈ K.
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On the class of b almost order (L) sets in Banach lattices
Positivity, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oughajji, Fatima Zahra, Moussa, Mohammed
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A Characterization of Ordered Sets and Lattices via Betweenness Relations
Results in Mathematics, 2004The authors establish a canonical one-to-one correspondence for a set with at least 3 elements. The one-to-one correspondence is between all betweenness relations satisfying certain axioms and all pairs of inverse ordering ``\(\)'' defined on orderings for which the corresponding Hasse diagram is connected and all maximal chains contain at least 3 ...
Düvelmeyer, Nico, Wenzel, Walter
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Distributive and completely distributive lattice extensions of ordered sets
International Journal of Algebra and Computation, 2018It is known that a poset can be embedded into a distributive lattice if, and only if, it satisfies the prime filter separation property. We describe here a class of “prime filter completions” for posets with the prime filter separation property that are completely distributive lattices generated by the poset and preserve existing finite meets and joins.
Wilmari Morton, Clint J. van Alten
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On Lattices Embeddable into Lattices of Order-Convex Sets. II Star-like Posets
Order, 2010The authors continue the study of lattices that embed in lattices of order-convex subsets of posets. This paper is a continuation of Part I [Int. J. Algebra Comput. 17, No. 8, 1667--1712 (2007; Zbl 1152.06002)]. A poset is \textit{tree-like} if (i) whenever \(a, b \in P\) and \(a\) is majorized by \(b\) there is an ascending path from \(a\) to \(b\) in
Marina V. Semenova +1 more
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Partially Ordered Sets and Lattices
2009In this chapter we present some basic facts about partially ordered sets and lattices which are fundamental for our study of lattice-ordered groups, rings, and modules. The material presented includes Zorn’s Lemma and some of its equivalences in Section 1.1, standard characterizations of distributive lattices and Boolean algebras in Section 1.2, and ...
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Extending a Partially Ordered Set: Links with its Lattice of Ideals
Order, 1999Given a poset \(P\) on a set \(X\) it naturally defines a family \(E(P)\) of posets on \(X\) which extend \(P\), i.e., if \(x\leq y\) in \(P\) and if \(Q\in E(P)\), then \(x\leq y\) in \(Q\) also. There are many interesting connections between \(E(P)\) and \(I(P)\), the lattice of ideals of \(P\), e.g.
Philippe Baldy +2 more
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On the Partially Ordered Set of Prime Ideals of a Distributive Lattice
Canadian Journal of Mathematics, 1971For a distributive lattice L, let denote the poset of all prime ideals of L together with ∅ and L. This paper is concerned with the following type of problem. Given a class of distributive lattices, characterize all posets P for which for some . Such a poset P will be called representable over.
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Suatu Kajian Tentang Soft Set Terurut Lattice (Lattice Ordered Soft Set) [PDF]
, 2023 Teori soft set pertama kali diperkenalkan oleh Molodsov sebagai suatu metode untuk menangani ketidakpastian. Metode ini mengkaji mengenai pengelompokan objek-objek yang memenuhi atau tidak memenuhi suatu parameter tertentu. Namun, dalam teori soft set tidak terdapat urutan dalam himpunan parameternya sehingga dikaji suatu teori yaitu lattice ordered ...
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On partially ordered sets embeddable in a free lattice
Algebra Universalis, 1984For elements p, p' of a poset P, write \(p\sim p'\) provided ...
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