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Topic: Primary ideal

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	PlanetMath: primary ideal
		This is clearly a generalization of the notion of a prime ideal, and (very) loosely mirrors the relationship in
		It is clear that every prime ideal is primary.
		This is version 2 of primary ideal, born on 2004-03-12, modified 2004-03-23.
	planetmath.org /encyclopedia/PPrimary.html (81 words)

	The Radical of a Primary Ideal
		Recall that the radical of an ideal is the intersection of prime ideals containing said ideal.
		Thus the radical of a prime ideal p is p, as that is the intersection of all prime ideals containing p.
		All elements are nilpotent or units, r/h is a primary ring, and h is a primary ideal.
	www.mathreference.com /id-pry,radp.html (558 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-17)
		He also defined the prime ideal associated to a primary ideal, and proved the existence of a primary decomposition of an arbitrary ideal in a rings of polynomials.
		In a ring of polynomials, the ideals of the principal series are unmixed or, in modern terminology, a ring of polynomials is a Cohen–Macaulay ring.
		By combining the finite basis condition for any ideal with the maximum condition, that is, the ascending chain condition for ideals (a ring with this property is called Noetherian), she obtained in its most general form the Lasker–Macaulay theory of primary decompositions, which had previously been especially computational and cumbersome.
	eom.springer.de /C/c023370.htm (1870 words)

	Primary Rings and Ideals (Site not responding. Last check: 2007-10-17)
		Primary ideals are a generalization of prime ideals; hence prime ideals are primary.
		Assume r/h is a primary ring, and x is an element not in h, and xy lies in h.
		Therefore g is primary, and the contraction of a primary ideal is primary.
	www.mathreference.com /id-pry,intro.html (463 words)

	Economic Issues No. 33 - Educating Children in Poor Countries
		In an ideal world, primary education would be universal and publicly financed, and all children would be able to attend school regardless of their parents' ability or willingness to pay.
		Public resources may be diverted from primary education to institutions of higher education that serve the governing elite or shifted out of education altogether and into other projects—say, military buildup—favored by elites seeking to protect their interests.
		Statistics show that primary school enrollment and completion rates are low in many low-income countries, where underfinanced budgets, weak administrative capacity in the government bureaucracy, and lack of political will—indeed, political opposition to broadening access to educational opportunities—can deny children of poor parents an education.
	www.imf.org /external/pubs/ft/issues/issues33/index.htm (4157 words)

	Radical and Decomposition of Ideals
		Given an ideal I of a polynomial ring P over a field, return the radical of I. The radical R of I is defined to be the set of all polynomials f in P such that f^n in I for some n >= 1.
		Given an ideal I of a polynomial ring over a field, return the prime decomposition of the radical of I. This is equivalent to applying the function PrimaryDecomposition to the radical of I, but may be a little more efficient than using that method.
		Given an ideal I of a polynomial ring P over a field, return a probabilistic prime decomposition of the radical of I as a sequence of ideals of P. This function is like the function RadicalDecomposition except that the ideals returned may not be prime, but the time taken may be much less.
	www.math.lsu.edu /magma/text1123.htm (1115 words)

	The Saturation of a Prime Power
		This is one of the primary ideals in the decomposition of p
		One of the primary ideals is p primary.
		Apply second uniqueness and h is the p primary ideal that participates in the decomposition of j.
	www.mathreference.com /id-pry,psat.html (406 words)

	Performance Welding Racing Headers
		Primary tube sizing and length is very much determined using the actual power of the engine and at what RPM the engine is used at in your particular racing application.
		Therefore there is no true ideal length primary tube, as it's impossible to change this length as it's accelerating your racecar.
		The primary tube length is dictated by what RPM the engine is run at to obtain these power levels, with the vehicle weight, transmission, torque converter, and type of racing playing a dominating role.
	performanceweldingheaders.com /primary.htm (626 words)

	NIDA - What's New - Past Meetings - Primary Care and Drug Abuse: A Research-Setting Round Table Seminar
		Primary care (defined as “integrated and accessible health services provided by primary care clinicians [generally, physicians, nurse practitioners, and physician assistants]”) is the gateway for public health interventions.
		Leaders in primary care and other sectors have become increasingly aware that the historical definition of PC is inconsistent with current realities of medical care organization, financing, and preferences of patients and physicians.
		In one study of 29 adults, alcoholism treatment in primary care with naltrexone led to decreased drinking; in a randomized trial comparing buprenorphine treatment in primary care versus specialty treatment, treatment retention rates were higher, opioid use was less, and abstinence was greater in those in the PC program.
	www.drugabuse.gov /whatsnew/meetings/primarycare.html (6601 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-17)
		of integers a primary ideal is an ideal of the form
		In commutative algebra an important role is played by the representation of an arbitrary ideal of a commutative Noetherian ring as an intersection of a finite number of primary ideals — a primary decomposition.
		In the non-commutative case this is not true and therefore attempts have been undertaken to construct various non-commutative generalizations of the notion of primarity.
	eom.springer.de /p/p074460.htm (218 words)

	Primary Decomposition (Site not responding. Last check: 2007-10-17)
		We have therefore shown that prime ideals that occur in an irredundant primary decomposition of (0) in the ring R are all annihilators of some element of R.
		We have shown that the associated primes are precisely the primes that occur as the radicals of the primary ideals in an irredundant primary decomposition.
		The primary ideal in an irredundant primary decompostion that corresponds to a minimal prime in R is uniquely determined.
	www.imsc.res.in /~kapil/geometry/caag/primary.html (1441 words)

	An Ideal Vision of Primary Care
		There is no one perfect model for primary care, as the context of family and community require that providers and provider systems adapt to reflect the needs and values of communities across the country that vary widely in terms of age, ethnic identity, cultural values, and health problems.
		Primary care providers have a responsibility to do the best they can for patients, to educate patients fully, to share decision making with patients, and to respond to issues and concerns raised by patients.
		They must understand the range of services and supports available to the patient in their family and community, and work with the patient to use these supports as constructive assets in managing the patient’s health care.
	www.primarycaresociety.org /aa3.htm (506 words)

	commalg.org - the center for commutative algebra
		In this paper we present a procedure for computing the coefficient ideals, in particular the Ratllif-Rush closure, of a $\max-$primary ideal $I \subset R$.
		Our principal focuses are the similarities between the ideal structure of the Nagata and Kronecker semistar rings and between the natural semistar operations that these two types of function rings give rise to on $D$.
		We study the ideal I_n of all algebraic relations among the m_{ij}, and the algebraic variety S(K_n) of dimension 2n-3 (the slope variety of the complete graph) which it defines.
	www.commalg.org /preprints/2003_02.shtml (1397 words)

	Radical and Decomposition of Ideals
		The radical R is also an ideal of P. Currently the algorithm works for any zero-dimensional ideal over any field, but the algorithm works for non zero-dimensional ideals only if the coefficient field is perfect (which means in Magma that the coefficient field must have characteristic zero).
		The intersection of the ideals of Q is I. The ideals of P are the associated primes of Q; i.e.
		The intersection of the ideals of P is the radical of I. P is minimal: no ideal of P contains the intersection of the rest of the ideals of P. P is sorted so that P is always unique.
	www.math.ufl.edu /help/magma/text358.html (691 words)

	ABSTRACT ALGEBRA ON LINE: Ideal Theory of Commutative Rings
		I is the intersection of all prime ideals of R that contain I. In any principal ideal domain, our next definitions both reduce to the statement that the ideal in question is generated by a power of an irreducible element.
		Furthermore, in any such representation of I as an intersection of primary ideals, there must be n ideals, and the set of their associated prime ideals must be the same.
		One important consequence of the generalized principal ideal theorem is that any Noetherian ring satisfies the descending chain condition for prime ideals.
	www.math.niu.edu /~beachy/aaol/commutative.html (2296 words)

	Sp0 and Sph
		In summary, p is minimal iff p = rad(Sp0), iff Sp0 is p primary - whence Sp0 is the smallest p primary ideal.
		Thus we have "normalized" the primary ideals, at least for the minimal primes.
		I'm referencing a section that is yet to come, but the saturation of j through a minimal prime p containing j produces the p primary ideal that contributes to the intersection.
	www.mathreference.com /id-pry,sph.html (1292 words)

	Does Conceivability Entail Possibility?
		Primary positive conceivability implies primary negative conceivability, for both the prima facie and ideal versions, but the reverse is not obviously the case.
		Primary intensions are grounded in the epistemic evaluation of statements in worlds: that is, the evaluation of statements in worlds considered as actual.
		The primary intension of a statement could be defined in various ways, but the most useful definition is that in terms of a priori entailments: the primary intension of S is true at W if the material conditional "if W is actual, then S" is a priori.
	consc.net /papers/conceivability.html (21164 words)

	SparkNotes: An Ideal Husband: Themes, Motifs, and Symbols
		As the title might suggest, An Ideal Husband's primary theme is marriage, a common premise for the potboiler melodramas of Wilde's day.
		Lady Chiltern's primary foil, however, is of course the "lamia-like"—that is, half-snake and half-female—Mrs.
		Consequently, the apparently frivolous epigram becomes the primary vehicle by which the play mocks the values and mores of the contemporary popular stage.
	www.sparknotes.com /drama/idealhusband/themes.html (1819 words)

	[No title]
		If Q is a primary ideal in a commutative ring A and c (Q, then ((Q:c) = (Q and (Q:c) is primary.
		If I = Q1 (Q2 (((Qr is an irredundant primary decomposition of an ideal I in a commutative ring A, prove that a prime ideal P (A is the radical of one of the Qj if and only if for some c (A the ideal (I:c) is P-primary.
		Show that every non-zero ideal can be expressed uniquely as a product of primary ideals with distinct radicals.
	www.stanford.edu /class/math210b/MATH210bASSIGN7.doc (341 words)

	Untitled Document (Site not responding. Last check: 2007-10-17)
		The Academy for Ideal Education Primary Campus Library was established in September, 2000 with a grant from the Charity Committee of Logistics Management Institute, McLean, Va. The funding was issued based on a proposal submitted by Ms.
		With this grant, Ideal was able to obtain the core collection, establish sufficient space and acquire the needed furniture.
		The librarian dedicates her time to the school as part of her commitment to the Ideal community.
	students.cua.edu /02tyler/idealweb/aboutlib.html (115 words)

	[No title]
		Given a statement S and a world W, the primary intension (or epistemic intension) of S returns the truth-value of S in W considered as actual (p.163).
		S is ideally conceivable when S is conceivable on ideal rational reflection.
		Further, ideal primary negative conceivability entails primary possibility, and secunda facie primary positive conceivability is an extremely good guide to primary possibility.
	www.ceu.hu /phil/Miscevic/revGendler.doc (2434 words)

	Primary Key (Site not responding. Last check: 2007-10-17)
		A table cannot have more than one PrimaryKey, and should not have zero primary keys (this is usually but not always enforced in RDBMS systems).
		Often the term PrimaryKey is used to refer to a set of columns which is a strict subset of all of the columns in the table; and in many cases it is assumed that the PrimaryKey consists of a single column.
		In a normalized database, primary key values are the only values that should appear multiple times in the database.
	c2.com /cgi-bin/wiki.pl?PrimaryKey (301 words)

	Curriculum Vitae of Anna Guerrieri
		Primary decompositions of Jacobian ideals: an application of 1-genericity (with I. Swanson) Jour.
		Primary decomposition and Jacobian ideals of multilinear forms, one hour invited talk in the program Young Algebra Seminar organized by the Department of Mathematics of the University or Rome - Tor Vergata (February, 8, 1999).
		On the primary decomposition of the jacobian ideal of trilinear forms
	univaq.it /~guerran/vita.html (1156 words)

	All Electronics Corp - Parts, Supplies and Components
		Note: We have been told recently that in order to use this transmitter as a primary control, it is necessary to use a micro controller module to split and amplify the received signal into six individual channels.
		Ideal for high-density wiring areas, small conduits, under carpet use or swivel-arm brackets where flexibility is a factor.
		Marketed as a supplemental brake light for cars, trucks and motorcycles, the 12Vdc light-bar is ideal for any attention-getting application.
	www.allelectronics.com (610 words)

	IDEAL Campus Locations
		The IDEAL program allows you to finish what you started—build upon what you have accomplished in your life.
		With your schedule, we know that convenience is a primary concern.
		IDEAL offers undergraduate degree programs in convenient locations throughout Fairfield County.
	www.bridgeport.edu /pages/2260.asp (78 words)

	amaxa \| FAQ: Why is the Nucleofector technology ideal for primary cells and difficult-to-transfect cell lines?
		«Why is the Nucleofector technology ideal for primary cells and difficult-to-transfect cell lines?»
		Therefore, the technique is the ideal tool for primary cells, even for non-dividing cells such as neurons.
		In cell lines as well as primary cells, this yields gene expression shortly after transfection and in many cases transfection efficiencies of over 50% can be detected in as little as 2-4 hours.
	www.amaxa.com /faqdetails.html?&no_cache=1&tx_mwaxfaq_pi2[id]=3&tx_mwaxfaq_pi2[search]=&tx_mwaxfaq_pi2[page]=1&no_cache=1&tx_mwaxfaq_pi2[advancedsearch]=&tx_mwaxfaq_pi2[category_type_operator]=&tx_mwaxfaq_pi2[category]=&tx_mwaxfaq_pi2[cell_type_operator]=&tx_mwaxfaq_pi2[cell_type]=&tx_mwaxfaq_pi2[product_operator]=&tx_mwaxfaq_pi2[product]=&tx_mwaxfaq_pi2[keyword]= (110 words)

	Untitled Document (Site not responding. Last check: 2007-10-17)
		This committee consists of the assistant principal, the librarian, a primary campus teacher familiar with the grade(s) for which the material is considered appropriate and two (2) PTA representatives.
		Concerns will be considered when this form is completed and returned to the assistant principal.
		Academy for Ideal Education, 1501 Gallatin St., NW Washington, DC 20011
	students.cua.edu /02tyler/idealweb/reconsider.html (102 words)

	Atlas: A classification of primary ideals in a non commutative valuation ring by Hidetoshi Marubayashi (Site not responding. Last check: 2007-10-17)
		Atlas: A classification of primary ideals in a non commutative valuation ring by Hidetoshi Marubayashi
		(P2) P is a lower limit prime ideal.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-48.
	atlas-conferences.com /cgi-bin/abstract/cacv-48 (275 words)

	Primary Care Jobs & Positions - Primary Care Physician Job Search
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		Our system will match your mini-profile with Primary Care Jobs available nationwide, and display all of your available options.
		Please click here to match your mini-profile to our nationwide database of currently available Primary Care Jobs.
	www.primarycarejob.com (100 words)

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