
	Where results make sense

Topic: Distributive lattice

Related Topics

Boolean algebra

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Distributive lattice - Wikipedia, the free encyclopedia
		For example, an element of a distributive lattice is meet-prime iff it is meet-irreducible, though the latter is in general a weaker property.
		It states that every finite distributive lattice is isomorphic to the lattice of lower sets of the poset of join-prime (equivalently: join-irreducible) elements.
		The verification that this structure is a distributive lattice with the required universal property is routine.
	en.wikipedia.org /wiki/Distributive_lattice (1185 words)

	Distributivity - Wikipedia, the free encyclopedia
		In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra.
		Multiplication of numbers is distributive over addition of numbers, for a broad class of different kinds of numbers ranging from natural numbers to complex numbers and cardinal numbers.
		Distributivity is most commonly found in rings and distributive lattices.
	en.wikipedia.org /wiki/Distributive (771 words)

	Lattice (order) (Site not responding. Last check: 2007-10-21)
		Lattices constitute one of the the most prominent representatives of a series of "lattice-like" structures which admit order-theoretic as well as algebraic descriptions, such as semilattices, Heyting algebras, or Boolean algebras.
		Using the standard definition of universal algebra, a free lattice over a generating set S is a lattice L together with a function i:S→L, such that any function f from S to the underlying set of some lattice M can be factored uniquely through a lattice homomorphism f° from L to M.
		These conditions basically amount to saying that there is a functor from the category of sets and functions to the category of lattices and lattice homomorphisms which is left adjoint to the forgetful functor from lattices to their underlying sets.
	www.sciencedaily.com /encyclopedia/lattice__order_ (2523 words)

	Distributive lattice (Site not responding. Last check: 2007-10-21)
		In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima.
		Most of these apply to partially ordered sets that are at least lattices, but the concept can in fact reasonably be generalized to semilattices as well.
		For a complete lattice, arbitrarysubsets have both infima and suprema and thus infinitary meet and join operations are available.
	www.therfcc.org /distributive-lattice-84917.html (717 words)

	PlanetMath: distributive lattice (Site not responding. Last check: 2007-10-21)
		A lattice is said to be distributive if it satisifes either (and therefore both) of the distributive laws:
		Examples of distributive lattices include Boolean lattices and totally ordered sets.
		This is version 13 of distributive lattice, born on 2002-02-24, modified 2005-02-04.
	planetmath.org /encyclopedia/DistributiveLattice.html (59 words)

	Distributivity (Site not responding. Last check: 2007-10-21)
		Multiplication of numbers is distributive over addition of numbers a broad class of different kinds of ranging from natural numbers to complex numbers and cardinal numbers.
		A lattice is another kind of algebraic structure with two binary operations ^ and If either of these operations (say ^) over the other (v) then v must distribute over ^ and the lattice is distributive.
		Rings and distributive lattices are both special of rigs certain generalisations of rings.
	www.freeglossary.com /Distributivity (705 words)

	Distributivity (order theory) (Site not responding. Last check: 2007-10-21)
		Thus any distributive meet-semilattice in which binary joins exist is a distributive lattice.
		For a complete lattice, arbitrary subsets have both infima and suprema and thus infinitary meet and join operations are available.
		Distributivity is a basic concept that is treated in any textbook on lattice and order theory.
	www.sciencedaily.com /encyclopedia/distributivity__order_theory_ (807 words)

	PlanetMath: lattice (Site not responding. Last check: 2007-10-21)
		Thus a lattice is a commutative band with either operation.
		While many nice lattices, such as face lattices of polytopes, are distributive, there are also important classes of lattices, such as partition lattices, that are usually not distributive.
		This is version 9 of lattice, born on 2002-02-24, modified 2004-02-16.
	planetmath.org /encyclopedia/Lattice.html (143 words)

	Distributive law (Site not responding. Last check: 2007-10-21)
		Multiplication of numbers is distributive over addition of numbers, for a broadclass of different kinds of numbers ranging from natural numbers to complex numbers and cardinal numbers.
		For integers, the greatest common divisor is distributive over the least common multiple, and vice versa: gcd(a,lcm(b,c)) =lcm(gcd(a,b),gcd(a,c)) and lcm(a,gcd(b,c)) =gcd(lcm(a,b),lcm(a,c)).
		Rings and distributive lattices are both special kinds of rigs,certain generalisations of rings.
	www.therfcc.org /distributive-law-210616.html (698 words)

	Distributive lattice - TheBestLinks.com - Axiom of choice, Boolean algebra, Iff, Idempotent, ... (Site not responding. Last check: 2007-10-21)
		A lattice is distributive iff non of its sublattices is isomorphic to M
		Furthermore, every distributive lattice is also modular (see also the main article on lattices).
		The important insight from this characterization is that the identities (equations) that hold in all distributive lattices are exactly e that hold in all lattices of sets in the above sense.
	www.thebestlinks.com /Distributive_lattice.html (1206 words)

	Science Fair Projects - Distributive lattice
		For example, a lattice L is distributive iff the following holds for all elements x, y, z in L:
		The free distributive lattice over a set of generators G can be constructed much easier than a general free lattice.
		The check that this structure is a distributive lattice with the required universal property is routine.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Distributive_lattice (1336 words)

	Research Interests (Site not responding. Last check: 2007-10-21)
		A lattice is defined as an algebra on a nonempty set with binary operations join and meet which are commutative and associative, and satisfy the absorption identities.
		Lattices theory is well-developed (G. Birkhoff's book 1967 the last edition) and figure in many branches of mathematics and computer science.
		The 2-dimension of a poset or a lattice P, is the smallest integer k which embeds P in the boolean lattice 2^k.
	www.lirmm.fr /~nourine/research-en.html (503 words)

	Distributivity (Site not responding. Last check: 2007-10-21)
		Distributivity is most commonly found in ringss and distributive lattices.
		Rings and distributive lattices are both special kinds of rigss, certain generalisations of rings.
		In several mathematical areas, generalized distributivity laws are consdidered.
	www.wikiverse.org /distributivity (564 words)

	[No title]
		A complemented distributive lattice is described in several files at this Website as a t-lattice, respecting the measure of type (a.k.a.
		However, although the distributive lattice -- in which not every element is complemented -- is recognized in standard lattice theory, the above decomposition will not fit it, and no attempt has been done to remedy this omission.
		distributive lattice) has at least one nonatomic element which is not join-reducible, yet no operation appears in the literature to provide it.
	members.fortunecity.com /jonhays/spectral.htm (542 words)

	The Basic Theory of Ordering Relations: A Supplement to Quantum Logic and Probability Theory
		On the other hand, the lattice of subspaces of a vector space is not distributive, for reasons that will become clear in a moment.
		In particular, the subspace lattice of a vector space (of dimension greater than 1) is not distributive.
		If a lattice is distributive, it may be that some of its elements have a complement, while others lack a complement.
	plato.stanford.edu /entries/qt-quantlog/supplement2.html (1398 words)

	Finite Algebra and Multiple-Valued (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		[111] H.Gaitan, Quasivarieties of distributive p-algebras, Algebra Universalis 29 (1992), 485--494.
		5 The Frattini sublattice of a finite distributive lattice (context) - Abad, Adams - 1994
		5 The Frattini sublattice of a distributive lattice (context) - Adams - 1973
	citeseer.ist.psu.edu /97324.html (259 words)

	56 #2891 (Site not responding. Last check: 2007-10-21)
		In case the lattice is an ordinal sum of two complete atomic Boolean subspace lattices, a sharp upper bound for the rank of single elements is produced.
		A subspace lattice L on X is said to have the strong rank-one density property if the identity operator on X belongs to the closure in the strong operator topology of the algebra generated by the rank-one operators leaving invariant every element of L.
		A particular pentagon lattice is defined on H Å H, formed from the graphs of A and -A and the space G(A) Å M. This lattice is called P(A; M).
	www.math.uoc.gr /~lambrou/MR.htm (4146 words)

	Maybe this Explains the Economic Cycle... best Distributive Lattice (Site not responding. Last check: 2007-10-21)
		distributive lattice distributive lattice A Lattice is said to be...
		Distributive Lattice -- from MathWorld Distributive Lattice -- from MathWorld A lattice which satisfies the identities (x\wedge y)\vee(x\wedge z)=x\wedge(y\vee z) (x\vee y)\wedge(x\vee z)=x\vee(y\wedge z) is said to be distributive.
		of arbitrary lattices, one can choose to consider a distributive lattice L either as a structure of order theory or of...
	ascot.pl /th/Fourier3/Distributive-Lattice.htm (485 words)

	Distributive Lattice Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-21)
		Looking For distributive lattice - Find distributive lattice and more at Lycos Search.
		Find distributive lattice - Your relevant result is a click away!
		Look for distributive lattice - Find distributive lattice at one of the best sites the Internet has to offer!
	www.karr.net /search/encyclopedia/Distributive_lattice (1353 words)

	All finite distributive lattices occur as intervals between Hausdorff topologies
		forms a lattice under inclusion, in which the meet of two topologies is their intersection, while the join is the topology with their union as a sub-basis.
		In this paper we are concerned with the local structure of this lattice.
		Hence a finite lattice can be realized as such an interval if and only if it is distributive.
	pear.math.pitt.edu /mathzilla/Examples/lattices.xml (830 words)

	Generating Random Elements of Finite Distributive Lattices - Propp (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice.
		The method is based on ideas of the author and David Wilson for using "coupling from the past" to remove initialization bias from Monte Carlo randomization.
		The article describes several applications to specific kinds of combinatorial objects such as tilings, constrained lattice paths, and alternating-sign matrices.
	citeseer.ist.psu.edu /propp96generating.html (632 words)

	MT4850 (Site not responding. Last check: 2007-10-21)
		appreciate the different classes of lattice that are described in the course and thereby begin to see the relevance of lattice theory to other parts of algebra.
		to recognize the proper status of a boolean algebra as a complemented distributive lattice.
		Lattice Theory; first concepts and distributive lattices: G Grätzer, (Freeman, 1971).
	www-maths.mcs.st-andrews.ac.uk /ug/hon4/MT4850.shtml (243 words)

	Definition of Distributive lattice
		A lattice (L, $\vee, \wedge) is$ distributive if the following additional identity holds for all x, y, and z in L:
		The first observation is that, using the laws of distributivity, every term formed by the binary operations $\vee and \wedge on a set of generators can be transformed into the following equivalent normal form:$
		The list of authors can be found here.
	www.wordiq.com /definition/Distributive_lattice (1278 words)

	distributive lattice - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "distributive lattice" is defined.
		Distributive Lattice : Eric Weisstein's World of Mathematics [home, info]
		distributive lattice : FOLDOP - Free On Line Dictionary Of Philosophy [home, info]
	www.onelook.com /?w=distributive+lattice (104 words)

	Embedding Distributive Lattices Preserving 1 Below a Nonzero Recursively Enumerable Turing Degree (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		Abstract: this paper, we show that they can be, by proving that for every nonzero a 2 R, every countable distributive lattice can be embedded into R(a) preserving 1 (Theorem 18).
		The long gap between the appearance of [16] and our paper is perhaps explained by the fact that the techniques of Lachlan's paper have not been wellunderstood.
		9 Lattice nonembeddings and initial segments of the recursivel..
	citeseer.csail.mit.edu /67327.html (469 words)

	PlanetMath: distributive (Site not responding. Last check: 2007-10-21)
		, then it is said to be distributive over
		This is version 9 of distributive, born on 2003-07-22, modified 2004-10-17.
		Object id is 4493, canonical name is Distributive.
	www.planetmath.org /encyclopedia/LeftDistributive.html (62 words)

	FREECD
		I'll illustrate the RANK measure of a lattice by a simple case: 6-CDL, the complemented distributive lattice on factors of 6.
		(Two elements of a lattice are mutually complementary if their only "connections" are at the "bottom" & "top" of the lattice, as is the case here with 2 & 3.
		Elements of RANK 1 (2 & 3, above) are known as "atoms" of a lattice.
	members.fortunecity.com /jonhays/freecdrk.htm (264 words)

	EconPapers: research articles: A class of multipartner matching markets with a strong lattice structure
		However, the lattice operations were not simple and not distributive.
		Recently Alkan [3] showed that if one introduces quotas together with a monotonicity condition then the set of stable matchings is a distributive lattice under a natural definition of supremum and infimum for matchings.
		Stable matchings also have the polarity property (supremum with respect to one side is identical to infimum with respect to the other side) and a property we call {\it complementarity}.
	netec.mcc.ac.uk /WoPEc/data/Articles/sprjoecthv:19:y:2002:i:4:p:737-746.html (324 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The Lindenbaum algebra generated by the Abramsky finitary logic is a distributive lattice dual to an SFP-domain obtained as a solution of a recursive domain equation.
		We prove that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain.
		As a consequence soundness and completeness of the infinitary logic is obtained for a class of transition systems that is computational interesting.
	homepages.cwi.nl /~marcello/Abs/alxts (118 words)

	Atlas: Boolean products and canonical extensions of bounded distributive lattice expansions by Bjarni Jonsson
		Canonical extensions of bounded distributive lattice expansions have been defined and investigated under some conditions on the auxiliary operations, but here these operations will be completely arbitrary.
		DL :The category of all doubly algebraic, bounded distributive lattices, with complete homomorphisms as the morphisms.
		The name of a category will also be used as a collective name for its objects, E. g., a bounded distributive lattice will be referred to as a DL.
	atlas-conferences.com /cgi-bin/abstract/caig-87 (1139 words)

Try your search on: Qwika (all wikis)