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Topic: Descending chain condition

	Ascending chain condition - Wikipedia, the free encyclopedia
		The ascending chain condition on P is equivalent to the maximum condition: every nonempty subset of P has a maximal element.
		Similarly, the descending chain condition is equivalent to the minimum condition: every nonempty subset of P has a minimal element.
		A totally ordered set that satisfies the descending chain condition is called a well-ordered set.
	en.wikipedia.org /wiki/Ascending_chain_condition (166 words)

	Artinian - Wikipedia, the free encyclopedia
		In mathematics, Artinian is an adjective that describes objects that satisfy particular cases of the descending chain condition.
		A ring is an Artinian ring if it satisfies the descending chain condition on ideals.
		The concept is named for Emil Artin, who classified all simple rings whose one-sided ideals satisfy the descending chain condition.
	en.wikipedia.org /wiki/Artinian (135 words)

	DESCENDING-PAGE 1
		He waited on the landing watching the steps of the escalators slowly descend toward him and, at the end of their journey, telescope in upon themselves and disappear.
		It was, of course, possible that he had to descend two flights of stairs for every floor of the department store.
		Because he was hungry and because he was tired and because the futility of mounting endless flights of descending escalators was, as he now considered it, a labor of Sisyphus, he returned, descended, gave in.
	www.scifi.com /scifiction/classics/classics_archive/disch/disch1.html (3875 words)

	philosophy notes
		Since the descending chain condition treats all left ideals the hypothesis of this theorem is phrased in second order rather than first order logic.
		The fact that a polynomial ring over a field is Noetherian yields to a descending chain condition on closed subgroups.
		Both proofs use the chain conditions and induction on rank as a substitute for cardinality.
	www.math.uic.edu /~jbaldwin/pub/phil.html (2052 words)

	Finite Rings (Site not responding. Last check: 2007-10-08)
		It is clear that such a ring satisfies the descending chain condition for ideals.
		The ring also satisfies the ascending chain condition; any ascending chain of ideals is constant after a finite stage.
		The given condition on f can be restated by saying that H(f) is a unit in the ring of formal power series and L(f) is in M[X] where M is the maximal ideal of the ring A.
	www.imsc.ernet.in /~kapil/geometry/caag/finite.html (2519 words)

	[No title]
		Hence the family (Zt)t2N is descending M = Z0 ' Z1 ' : : : ' Zt ' : : : and it is stationary at some t0, that is, Zt0 = Zt0+1 = : : :.
		Hence a descending family of algebraic subsets of X is stationary.
		The assumptions of Theorem 4.2 are satisfied as any descending family of algebraic sets is stationary, and under the assumptions of this corollary the sets considered in Definition 4.1 are algebraic as they can be expressed in terms of vanishing principal minors of algebraic functions.
	www.math.rutgers.edu /~sontag/wirth-scl.html (4745 words)

	PlanetMath: ascending chain condition (Site not responding. Last check: 2007-10-08)
		when ordered by inclusion) satisfies the ascending chain condition or ACC if there does not exist an infinite ascending
		Cross-references: descending chain condition, chain, infinite, satisfies, inclusion, subsets, collection, partially ordered set
		This is version 4 of ascending chain condition, born on 2001-11-23, modified 2004-05-01.
	planetmath.org /encyclopedia/AscendingChainCondition.html (72 words)

	Chains of Modules (Site not responding. Last check: 2007-10-08)
		If you like set theory, think of a chain as a map from the ordinals into the submodules of m, where the submodules increase or decrease as the ordinals advance.
		At approximately the same time, Artin (biography) explored modules with no infinite descending chains, and these modules are now called artinian.
		Another synonym for noetherian is "ascending chain condition", or ACC.
	www.mathreference.com /mod-acc,intro.html (236 words)

	Dilworth, Robert P. (1939-01-01) The structure and arithmetical theory of non-commutative residuated lattices. ...
		It is shown that under certain general conditions each of these operations may be defined in terms of the other.
		It is shown that each element of a modular lattice in which suitable chain conditions hold, may be represented as a product of irreducibles; and if there are two such decompositions, the number of irreducibles is the same and they are similar in pairs.
		In the first part the structure of ideal lattices in the vicinity of the unit element is characterized in terms of arithmetical and semi-arithmetical lattices.
	etd.caltech.edu /etd/available/etd-05222003-111959 (429 words)

	PlanetMath: descending chain condition (Site not responding. Last check: 2007-10-08)
		, ordered by inclusion) satisfies the descending chain condition or DCC if there does not exist an infinite descending
		Cross-references: ascending chain condition, chain, infinite, satisfies, inclusion, subsets, collection, partially ordered set
		This is version 3 of descending chain condition, born on 2001-11-23, modified 2004-05-01.
	planetmath.org /encyclopedia/DescendingChainCondition.html (72 words)

	Graduate Seminar
		One property people often ask as a first question about a ring is what are some basic properties of its ideals.
		One property that turns out to be quite useful in proving many basic results about a ring is contained in information concerning chains of ideals.
		Two seemingly dueling notions are the ascending chain condition (ACC) and the descending chain condition (DCC).
	www.math.uga.edu /~clint/vigre/semSu03.htm (662 words)

	Commutative Algebra at the University of Zimbabwe (Site not responding. Last check: 2007-10-08)
		The ascending chain condition and descending chain condition in rings.
		The relationship between maximal/minimal conditions and nilpotency in rings.
		The right/left annihilator of a subset of a ring.
	www.uz.ac.zw /science/maths/courses/hmth035.htm (118 words)

	Meant Condition
		It was a silver Celtic cross on a thick chain.
		As he kissed his way down my face and chest, the pendant followed not too far behind, retracing his lips' tender movements.
		Descending that Kerr county hill, she racked her overworked mind...
	swordsandknives.blogspot.com (1679 words)

	DCC (Site not responding. Last check: 2007-10-08)
		DCC may mean DCC, an Irish investments holding company.
		Descending chain condition in the field of order theory in mathematics
		DCC is also an abbreviation for Digital Content Creation.
	www.worldhistory.com /wiki/D/DCC.htm (155 words)

	Normal Structure and Characteristic Subgroups
		The lower central series for the group G. The series is returned as a sequence of subgroups.
		Since infinite polycyclic groups need not satisfy the descending chain condition for subgroups, computation of the lower central series may fail.
		The series is returned as a sequence of subgroups of G. Note that since polycyclic groups satisfy the ascending chain condition for subgroups, every polycyclic group G has a finite upper central series.
	www.math.lsu.edu /magma/text452.htm (829 words)

	Mark Teply: Curriculum Vita
		Ph.D. Fenrick - "Conditions under which all preradicals are torsion or perfect torsion radicals," December, 1973.
		"The Descending Chain Condition Relative to a Torsion Theory," (written jointly with R. Miller), Pacific J. Math.
		"Generalized Deviations of Posets with Applications to Chain Conditions on Modules," with T. Albu, International Symposium on Ring Theory, edited by Park et al., Trends in Mathematics, Birkhauser, Boston, 2001, pp.
	www.uwm.edu /People/mlteply/cv.html (1678 words)

	Abstract (Site not responding. Last check: 2007-10-08)
		In this paper, causal rational encoders over commutative rings are considered and a general criterion of Johannesson and Wan (see IEEE Trans.
		Theory, vol.39, p.1219-33, July 1993) is generalized to rings, which satisfy the descending chain condition.
		Moreover, a new simple test is presented that reduces the minimality question from the ring to the field case.
	www.isi.ee.ethz.ch /cgi-bin/srv?isipapa:isipap/tmitte-inspec-1995-2 (123 words)

	Descending
		Lengths of golden chain, bejeweled crowns, scepters and large vases laid on top of some of the piles as if in homage to long absent royalty.
		He pulled a large gold chain with a glittering ruby attached from the pile and placed it over his head.
		The creature had effectively pushed the girl's body into the mound of golden chain and coin in its effort to make her part of the amassed treasure.
	ausxip.com /fanfiction/m/minetohave2.html (17238 words)

	On Chains of Word Equations and Test Sets (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: Ehrenfeucht's Conjecture is equivalent with the ascending chain condition for word equations.
		A related conjecture concerns the descending chain condition for word equations.
		We show that if this conjecture holds then an arbitrary infinite language L possesses a finite subset F such that the language L \Gamma F (Update)
	citeseer.ist.psu.edu /440210.html (241 words)

	Letter A (Site not responding. Last check: 2007-10-08)
		That is, given two magnitudes with common ratio, there exists a multiple of either esceeding the other.
		A module (PL) fulfilling descending chain condition (PL): every decreasing sequence of submodules(PL) approaches constancy.
		An autonomous ODE is independent of the intial condition so that all particles pass through a given point of phase space (PL)..
	members.fortunecity.com /jonhays/letterA.htm (3975 words)

	The Base Ring
		During the ring setting the term order will be checked to be noetherian (i.e.
		to fulfill the descending chain condition) provided the switch noetherian ; is on (the default).
		The same applies turning noetherian on : If the term order of the underlying base ring isn't noetherian the switch can't be turned over.
	www.uni-koeln.de /REDUCE/cali/node7.html (433 words)

	Fitting ideals for finitely presented algebraic dynamical systems (Site not responding. Last check: 2007-10-08)
		We consider a class of algebraic dynamical systems introduced by Kitchens and Schmidt.
		Under a weak finiteness condition - the Descending Chain Condition - the dual modules have finite resentations.
		Using methods from commutative algebra we show how the dynamical properties of the system may be deduced from the Fitting ideals of a finite free resolution of the finitely presented module.
	www.mth.uea.ac.uk /~h720/abstracts/abs23.html (161 words)

	Chain Story
		must be so worried and she really shouldn't worry in her condition." Again Ben tried to get up, but the room started spinning and he sank back.
		"I dunno what condition she's in and where she is, but I do know that if'n ya keep doin' this she'll hafta wait even longer ta see ya.
		Adam rolled his head until he was able to look at his younger brother and gauge his condition.
	www.bonanza-legacy.com /authors/chain004.html (10071 words)

	Subject Index (Site not responding. Last check: 2007-10-08)
		adjointness of realization and singular chain functor 646
		equation for the resolvent of empirical covariance matrices if the Lindeberg condition holds 69
		right Jordan chain of a matrix pencil 82
	www.elsevier.com /homepage/saj/523281/subject.htm (1223 words)

	HogBlog: July 2003 Archives
		Say a module M is Artinian if it satisfies the descending chain condition on submodules: every chain of submodules
		Let R be a ring, M a left R-module, K a submodule of M such that K and M/K are both Artinian.
		be any descending chain of submodules in M. Then this chain induces two other chains,
	www.koschei.net /blog/archives/2003_07.html (9641 words)

	MSU Math Department - Graduate (Site not responding. Last check: 2007-10-08)
		The Jacobson radical, the structure of semisimple rings with the descending chain condition.
		Evolutionary problems, stability of initial value problems, ADI methods, wave equations and first order hyperbolic systems.
		Elliptic problems, approximation of boundary conditions, multigrid methods.
	www.mth.msu.edu /Graduate/handbook_part5.html (960 words)

	A. Pillay
		Generic sets in definably compact groups (with Y. Peterzil) 2004 [.dvi file or.pdf file]
		A descending chain condition for groups definable in o-minimal structures (with A. Berarducci, M. Otero, Y. Peterzil) [.dvi file or.pdf file]
		Algebraic D-groups and Differential Galois Theory [.dvi file or.pdf file]
	www.math.uiuc.edu /People/pillay.html (408 words)

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