Results 231 to 240 of about 1,634,119 (265)

ON LATTICES EMBEDDABLE INTO LATTICES OF ORDER-CONVEX SETS: CASE OF TREES

International Journal of Algebra and Computation, 2007
We find a syntactic characterization of the class of lattices embeddable into convexity lattices of posets which are trees. The characterization implies that this class forms a finitely based variety.
Marina V. Semenova, Anna Zamojska-Dzienio   +1 more
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Ordered Sets and Lattices II

, 1992
This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed ...
Draskovicova, H, Fofanova, T S, Igoshin, V I   +2 more
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Endomorphism Classes of Ordered Sets, Graphs and Lattices

Order, 1998
Mathematical structures of a certain type with an underlying set \(X\) are considered; they form the class \(C\). If \(S\in C\), then \(\text{End} S\) is the set of endomorphisms of \(S\). The following question is considered: Which structures \(S'\in C\) on the set \(X\) have the property that \(\text{End} S\subseteq\text{End} S'\)? If for some \(S\in
Gibson, Peter, Zaguia, Imed
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On Lattice Embeddings for Partially Ordered Sets

Canadian Journal of Mathematics, 1954
Let 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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A Characterization of Ordered Sets and Lattices via Betweenness Relations

Results in Mathematics, 2004
The 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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Partially Ordered Sets and Lattices

2009
In 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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Distributive and completely distributive lattice extensions of ordered sets

International Journal of Algebra and Computation, 2018
It 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, 2010
The 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, Anna Zamojska-Dzienio   +1 more
openaire   +1 more source

Extending a Partially Ordered Set: Links with its Lattice of Ideals

Order, 1999
Given 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, Michel Morvan, Eric Thierry   +2 more
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Large Sets of Lattices without Order Embeddings [PDF]

Communications in Algebra, 2015
Let I and μ be an infinite index set and a cardinal, respectively, such that |I| ≤ μ and, starting from ℵ0, μ can be constructed in countably many steps by passing from a cardinal λ to 2λ at successor ordinals and forming suprema at limit ordinals. We prove that there exists a system X = {Li: i ∈ I} of complemented lattices of cardinalities less than ...
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