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Topic: Ideal order theory

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	Ideal (order theory) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		Ideals are of great importance for many constructions in order and lattice theory.
		In Stone's representation theorem for Boolean algebras, the maximal ideals (or, equivalently via the negation map, ultrafilters) are used to obtain the set of points of a topological space, whose clopen sets are isomorphic to the original Boolean algebra.
		Ideals were introduced first by Marshall H. Stone, who derived their name from the ring ideals of abstract algebra.
	en.wikipedia.org /wiki/Ideal_(order_theory) (1212 words)

	Ideal (ring theory) (Site not responding. Last check: 2007-10-21)
		An ideal can be used to construct a factor ring in a similar way as a normal subgroup in group theory can be used to construct a factor group.
		The concept of an order ideal in order theory is derived from the notion of ideal in ring theory.
		The sum and the intersection of ideals is again an ideal; with these two operations as join and meet, the set of all ideals of a given ring forms a lattice.
	hallencyclopedia.com /Ideal_(ring_theory) (1487 words)

	Ideal (ring theory) - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-21)
		In ring theory, a branch of abstract algebra, an ideal of a ring R is a subset I of R which is closed under R-linear combinations, in a sense made precise below.
		The concept of an order ideal that is known in order theory is derived from this notion is discussed in its dedicated article.
		The term "ideal" comes from the notion of ideal number: ideals were seen as a generalization of the concept of number.
	encyclopedia.learnthis.info /i/id/ideal__ring_theory_.html (1381 words)

	[No title]
		abstract algebra, an ideal is a special subset of a ring which generalizes important properties of integers.
		order ideal in order theory is derived from the notion of ideal in ring theory.
		The sum and the intersection of ideals is again an ideal; with these two operations as join and meet, the set of all ideals of a given ring forms a
	en-cyclopedia.com /wiki/Maximal_ideal (1185 words)

	Ideal (order theory) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Ideals are of great importance for many constructions in order and (Click link for more info and facts about lattice theory) lattice theory.
		Order theory knows many completion procedures, to turn posets into posets with additional (The state of being complete and entire; having everything that is needed) completeness properties.
		Ideals were introduced first by (Click link for more info and facts about Marshall H. Stone) Marshall H. Stone, who derived their name from the ring ideals of abstract algebra.
	www.absoluteastronomy.com /encyclopedia/i/id/ideal_(order_theory).htm (1510 words)

	Axiomatic set theory (Site not responding. Last check: 2007-10-21)
		Initially controversial, set theory has come to play the role of a foundations of mathematicsfoundational theory/ in modern mathematics, in the sense of a theory invoked to justify assumptions made in mathematics concerning the existence of mathematical objects (such as numbers or functions) and their properties.
		It is often asserted that axiomatic set theory is thus an adequate foundation for current mathematical practice, in the sense that ''in principle'' all proofs produced by the mathematical community could be written formally in set theory terms.
		The most frequent objection to set theory is the mathematical constructivismconstructivist view that mathematics is loosely related to computation and that naive set theory/ is being formalised with the addition of noncomputational elements.
	www.infothis.com /find/Axiomatic_set_theory (2596 words)

	Articles - Order theory (Site not responding. Last check: 2007-10-21)
		Orders appear everywhere - at least as far as mathematics and related areas, such as computer science, are concerned.
		These are graphs where the vertices are the elements of the poset and the ordering relation is indicated by both the edges and the relative positioning of the vertices.
		Directed complete partial orders (dcpos), that guarantee the existence of suprema of all directed subsets and that are studied in domain theory.
	www.gaple.com /articles/Order_theory (3992 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-21)
		Ideality is a faculty from the discipline of Phrenology.
		ideals are special subsets of a ring considered in abstract algebra.ideals appear in order theory and are a special kind of lower sets of an order.
		In mathematics, ideal theory is the theory of ideals in commutative rings; and is the precursor name for the contemporary subject of commutative algebra.
	www.alanaditescili.net /browse.php?title=I/ID/IDE (3910 words)

	Ideal Theory of Orders
		The ideal theory of definite orders over Z is highly developed, allowing enumeration of all classes of ideals locally free over an order S, which is assumed to be an Eichler order or for which the index in an Eichler order is of valuation at most 1 at each ramified prime of the algebra.
		Given an ideal I, returns the left order of I, defined as the ring of all elements of the quaternion algebra of I mapping I to itself under left multiplication.
		Given an ideal or order I, returns the conjugate ideal.
	www.math.lsu.edu /magma/text871.htm (876 words)

	Ideal (order theory)
		While this is the most general way to define an ideal for arbitrary posets, it was originally defined for latticess only.
		In this case, the following equivalent definition can be given: A non-empty subset I of a lattice (P,≤) is an ideal, iff it is a lower set that is closed under finite joins (suprema), i.e., for all x, y in I, we find that xy is also in I.
		The principal ideal p for a principal p is thus given by p = {x in P
	www.brainyencyclopedia.com /encyclopedia/i/id/ideal__order_theory_.html (1275 words)

	Topos Theory
		Press) Topos theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics.
		Topos theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas.
		It is not addressed to those who are trying to learn about topos theory for the first time, but rather to those who already have some acquaintance with the subject and who wish to deepen their understanding, or to learn about aspects of it which they have not previously encountered.
	www.wordtrade.com /science/mathematics/topostheory.htm (3716 words)

	Glossary of order theory (Site not responding. Last check: 2007-10-21)
		As explained in the article on completeness (order theory), any poset for which either all suprema or all infima exist is already a complete lattice.
		A partial order is a binary relation that is reflexive, antisymmetric, and transitive.
		A strict order is a binary relation that is antisymmetric, transitive, and irreflexive.
	www.free-download-soft.com /info/startup-manager.html (2564 words)

	Bohm & the implicate order
		They both admired quantum theory's ability to predict phenomena, but could not accept that it was complete and that it was impossible to arrive at any clearer understanding of what was going on in the quantum realm.
		The explicate order is a projection from higher dimensional levels of reality, and the apparent stability and solidity of the objects and entities composing it are generated and sustained by a ceaseless process of enfoldment and unfoldment, for subatomic particles are constantly dissolving into the implicate order and then recrystallizing.
		Bohm believed that life and consciousness are enfolded deep in the generative order and are therefore present in varying degrees of unfoldment in all matter, including supposedly 'inanimate' matter such as electrons or plasmas.
	ourworld.compuserve.com /homepages/dp5/bohm.htm (2158 words)

	Lattice_(order) (Site not responding. Last check: 2007-10-21)
		In mathematics, a lattice is a partially ordered set (or poset), in which all nonempty finite subsets have both a supremum (join) and an infimum (meet).
		The natural numbers in their common order are a lattice, the lattice operations given by the min and max operations.
		In domain theory, one is often interested in approximating the elements in a partial order by "much simpler" elements.
	www.freecaviar.com /search.php?title=Lattice_(order) (2466 words)

	Error Theory: Order to release Abu Ghraib photos ignores war powers (Site not responding. Last check: 2007-10-21)
		There are the implications of thinking straight about fact and value (ideal theory) and there are the implications of not thinking straight.
		Ideal theory is the foundation, error theory the daily battle.
		My analysis stands, but be apprised that the linked Opinion and Order is not from Hellerstein's latest ruling, as I stated, but is from a ruling that PRECEEDED the February 12th ruling.
	errortheory.blogspot.com /2005/05/order-to-release-abu-ghraib-photos.html (1085 words)

	IdEAL ORDER Psychic TV
		IdEAL ORDER was founded in 1982 as an outlet for anarchic/artistic activism by Elsie Russell and Jeffrey Harrington.
		In 1984 IdEAL ORDER Psychic TV began a nightly zapping of the CBS Evening News and the McNeil/Lehrer News Hour and constant telepathic harassment of the Reagan administration during televised news conferences and news show appearances.
		In November 1991 IdEAL ORDER Psychic TV began focusing on a once a week disruption of the CBS Evening News so that skeptical viewers might be able to compare the illuminated with the non-illuminated broadcasts.
	www.parnasse.com /idealarchive.html (3551 words)

	Applying TRIZ and the Theory of Ideal SuperSmart Learning to Computing Systems: Ultimate Ideal Autonomous Objects, ...
		I had described the Theory of Ideal SuperSmart Learning as similar to a “theory of everything for product, personal, business, and institutional development.” The goal of the theory is “to know and understand everything from nothing and in no time.” This goal is based on utopic ideality.
		The Theory of Ideal SuperSmart Learning in combination with TRIZ could be used as a resource for developing the following: new paradigms for computing systems; new thinking about objects; new framings for apparently unsolvable problems; new approaches to organizing ideas for strategic problem solving and innovation.
		The key proposals of this paper are more widespread use of the model of “ultimate ideal autonomous (autonomic) object” for computing systems as well as case study applications of tools of TRIZ and the Theory of Ideal Supersmart Learning in the area of computing.
	www.triz-journal.com /archives/2002/09/e (6319 words)

	KLUEDO - Algorithmic ideal theory
		In the second chapter we introduce standard bases (generalization of Gröbner bases to non-well-orderings), which are needed for applications to local algebraic geometry (singularity theory), and a method for computing syzygies and free resolutions.
		In the third chapter several algorithms for primary decomposition of polynomial ideals are presented, together with a discussion of improvements and preferable choices.
		The last chapter gives an elementary introduction to singularity theory and then describes algorithms, using standard bases, to compute infinitesimal deformations and obstructions, which are basic for the deformation theory of isolated singularities.
	kluedo.ub.uni-kl.de /volltexte/2000/794 (293 words)

	Order Stars and Linear Stability Theory -- from Mathematica Information Center
		Order stars are a powerful modern tool for the development and analysis of numerical methods.
		An introduction to the theory is provided here, set in the context of numerical methods for Ordinary Differential Equations.
		The implementation is discussed and examples are given to illustrate why a computer algebra system is an ideal environment for the exploration of order stars.
	library.wolfram.com /infocenter/Articles/3116 (110 words)

	Machine Learning (Theory) (Site not responding. Last check: 2007-10-21)
		At one extreme, the tradition in CS theory conferences is to provide essentially zero feedback.
		This is important for experimental testing of predictions because the distribution that observations are expected to come from is a part of the theory under test.
		In order to graduate, a phd student must live in an academic culture for a period of several years.
	hunch.net (6102 words)

	Legal Theory Blog
		Under such a theory, the Religion Clauses together should be read to protect minority religious beliefs and practices from government burdens, and to equalize the status of minority religions before the government with that of majority faiths.
		Theories about fairness will be covered in future installments of the Legal Theory Lexicon; today, we focus on arguments of policy and the theoretical question, “What does it mean to say that a rule would produce the best consequences?” One answer to that question is “utilitarianism,” a theory of enormous interest and influence.
		Ideal Rule Utilitarianism (IRU) says that you should act in accordance with the set of “ideal rules” that would maximize utility if everyone were actually to act in conformity with the rules.
	lsolum.blogspot.com (12744 words)

	Foucault, Order of Things (Site not responding. Last check: 2007-10-21)
		DQ demonstrates that truth is not to be found in the relation of written words to the world, but rather in the relation between the words themselves (48).
		III The theory of the verb (92ff): attribution: connection of representations; verb "to be"
		Thus, through the medium of language, things could be known, not because language was interwoven with the world (as in the Renaissance), but because through it, one could sketch of an order of representation based on one's thoughts (295).
	individual.utoronto.ca /bmclean/hermeneutics/Foucault/OT_outline.html (2456 words)

	Lattice (order) (Site not responding. Last check: 2007-10-21)
		This article treats the most basic definitions of lattice theory, including the case of bounded lattices, i.e., lattices that have unique top and bottom elements.
		For any set A, the collection of all subsets of A (called the power set of A) can be ordered via subset inclusion to obtain a bounded lattice.
		The non-zero natural numbers also form a lattice under the greatest common divisor and least common multiple operations, with the order relation representing divisibility.
	www.toshare.info /en/Distribute_lattice.htm (2265 words)

	Platonic Forms
		It is intended only to show that the theory is an intelligible and reasonable response to those problems.
		If A is a certain woman and B is a certain statue and both “A is beautiful” and “B is beautiful” are true statements, one might be tempted to think of the woman and the statue as participating in or sharing some common property–beauty, despite their being otherwise quite different.
		Because they are the patterns or ideal models to which we compare individual things or actions in order to determine how beautiful, just, or whatever, they are, he also refers to them as ‘Forms’ or ‘Ideas.’ For this reason, Plato’s view has been called idealism.
	www.soci.niu.edu /~phildept/Dye/forms.html (1378 words)

	Chaos and Order Page (Site not responding. Last check: 2007-10-21)
		This Philosopy is based upon the ideal of Balance between the forces of Chaos and order.
		To achieve these ideals, you must keep the forces of chaos and order in Balance.
		Total order is plain and boring, and Orderly people are often boring, dour, and controlled.
	www.geocities.com /Area51/4071/chaos.html (434 words)

	Theory : My ideal magazine (as a reader) (Site not responding. Last check: 2007-10-21)
		My ideal magazine would have stories that make me laugh out loud, cry just a bit, feel very happy at the end, and say to myself, "Now, _there's_ a keeper." Realms of Fantasy comes closest to this, which is why I still sub to it.
		First, let me say that I think my ideal magazine that I've seen so far has been the early Asimov's under George Scithers and with Isaac himself active with his editorials and answers to letters.
		And to get back on topic, that's my ideal magazine--a market that publishes all types of speculative fiction (fantasy, sci fi, horror, MR, fabulism, slipstream, surrealism, what-have-you) in a range of styles.
	www.speculations.com /rumormill?z=102889 (2961 words)

	Amazon.com: Books: Capitalism: The Unknown Ideal (Site not responding. Last check: 2007-10-21)
		In what is probably her best work of nonfiction, Ayn Rand sets out to provide a _moral_ basis for capitalism, a social/political order in which the human rights to life and property are respected and there are no (other) limitations on freedom of trade.
		That capitalism is today to some degree a _known_ ideal is in some measure due to the influence of Rand's ideas as represented in this volume.
		But in political theory, she was on firm ground -- and she knew it.
	www.amazon.com /exec/obidos/tg/detail/-/0451147952?v=glance (2211 words)

	Amazon.co.uk: Books: Effective Teaching in Schools: Theory and Practice (Site not responding. Last check: 2007-10-21)
		Recognising the shift of teacher training towards more teaching practice, the book combines depth and authoritative coverage in its treatment of the key theory with the conciseness and strongly practical focus students need to reflect creatively on their teaching experience.
		It is the ideal bridge between the theory students need to put their experience in context and the practice which allows them to build on theoretical work where it matters: in the classroom.
		It will also be an ideal companion volume to the author's Essential Teaching Skills in making an effective bridge from the theory to the practice of effective teaching.
	www.amazon.co.uk /exec/obidos/ASIN/0748728880 (790 words)

	NEW WORLD ORDER THEORY: THE NATURE OF THE UNIVERSE (Site not responding. Last check: 2007-10-21)
		This latin phrase translates as "New Secular Order." President Franklin D. Roosevelt, a 32nd degree Knight Templar and member of the Mystic Shrine and Scottish Rite, approved placement of the Craft's pyramid in the Great Seal of the United States on the dollar bill.
		Havelock Ellis, a student of Freud, who possessed a "contrary sexual feeling" and married a lesbian, took issue with Freud on the cause of homosexuality, claiming that homosexuality was inherited and could well be a sign of greatness.
		No scientific evidence has ever been found to support Ellis' theory, and it obviously must not have occurred to him that the "great" homosexuals who are prominent in history might have been much "greater" if they had not been homosexual.
	www.wealth4freedom.com /truth/6/NWOtheory.htm (3179 words)

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