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	Prime ideal - Wikipedia, the free encyclopedia
		In mathematics, a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers.
		Every maximal ideal is in fact prime; the converse is true in a principal ideal domain, but is not true in general.
		One use of prime ideals occurs in algebraic geometry, where varieties are defined as the zero sets of ideals in polynomial rings.
	en.wikipedia.org /wiki/Prime_ideal (804 words)

	ABSTRACT ALGEBRA ON LINE: Structure of Noncommutative Rings
		P, for any ideals A, B of R. A proper ideal I of the ring R is called a semiprime ideal if it is an intersection of prime ideals of R. A proper ideal P of the ring R is called a left primitive ideal if it is the annihilator of a simple left R-module.
		In a left Artinian ring, the notions of maximal ideal, primitive ideal, and prime ideal coincide.
		If P is a primitive ideal of the ring R, then there exists a division ring D and a vector space V over D for which R/P is isomorphic to a subring of the ring of all linear transformations from V into V. Proposition.
	www.math.niu.edu /~beachy/aaol/noncommutative.html (1031 words)

	Capuchin Friars Minor
		The dividing line between the two families was their adhesion to the primitive ideal of Franciscan poverty and simplicity; the Conventuals accepted revenues by papal dispensation; the Observants refused fixed revenues and lived by casual alms.
		To those who looked to the primitive custom of the order, such acceptances seemed but legalized betrayal of the rule, nor were these relaxations at any time allowed to pass without protest from the more zealous of the Observants.
		In this matter the friars of the reform were but reasserting the primitive Franciscan life; and it is to be noted that the method of their apostolate was also thoroughly in accord with what the early legends of the order tell us about St. Francis's method.
	www.catholicity.com /encyclopedia/c/capuchin_friars_minor.html (8375 words)

	[No title]
		An ideal $\ci$ of a general algebra $\ca$ being called regular if there is a unit in $\ca$ modulo $\ci$, namely an element $u \in \ca$ such that $a - a u$ and $a - u a$ are in $\ci$ for all $a \in \ca$ \cite{FD}.
		When thought of as a space of maximal ideals, $\hc$ is given the {\it Jacobson topology}~\index{Jacobson topology} (or {\it hull kernel topology}) producing a space which is homeomorphic to the one constructed by means of the Gel'fand topology.
		Conversely, if $\ci_F$ is primitive, it is not the intersection of two ideals different from itself, thus from (\ref{cor}) $F$ is not the union of two proper closed subsets, and from assumption $(ii)$, it is the closure of a one-point set.
	www.ma.utexas.edu /mp_arc/papers/97-62 (9392 words)

	The Spirituality of the Carmelites of the Ancient Observance: A summary of the lectures given by Blessed Titus Brandsma ...
		According to the testimony of the Dominican, Stephen of Salagnac, in the second half of the 13th century, the Institutio, even as apocryphal, remains a traditional paraphrase of the rule of life created by the Patriarch Aymeric of Malafay in 1156 to which allusion is made in the prologue of the Rule of 1205.
		The Order has always sought to preserve its proper ideal for as many of its sons as possible; it asks them to return with the greatest haste as soon as their exterior duties are accomplished to what is the direct and primary object of their calling.
		By the formulas in which it is expressed in the rule, Carmelite spirituality preserves the echo of the chivalric ideal of the crusaders who established it, almost in the same way in which the Exercises of Saint Ignatius retain in their wording something of the military ideal of the Knights of Pamplona.
	www.catholic-forum.com /saints/stt57003.htm (5924 words)

	Being Church In An Academic Setting
		This is not surprising since the Augustinian ideal of common life is inspired by the life of the primitive Christians who were neither religious nor ordained ministers of the priesthood.
		Luke's description of the primitive Christian community can be summarized into three points: (a) Fraternal sharing and distribution of goods; (b) fidelity to the memory of Christ; and (c) cultivation of Christian friendship.
		At the same time, the ideal that it presents is, for the Augustinian in the world, an impetus for the promtion of amore fraternal distribution of goods (cf.
	www.geocities.com /agilawan/mission/layspir.html (1819 words)

	Magnetics - More Complex Transformer Models
		Whenever ideal transformer primitives are combined, there MUST be a winding(s) which is (are) connected in parallel or in series, either on the input or the output side, to 'link' the all of the ideal transformers used in the simplest and most complex transformer primitive parts.
		Note that because the transformer primitives are ideal devices, there is no real detrimental effect in paralleling windings, except for the very minor effect of the resistors Rp, Rs and R1 in the primitive model.
		One way to do this is to add a transformer primitive to the model with a push-pull input winding, with a push-pull winding paralleled with the input winding, and a single isolated output winding (as in Figure 5) which has as its sole load the core model.
	www.beigebag.com /case_xfrmer_2.htm (2275 words)

	Essence as a Platonic ideal
		Platonic analysis aims to understand the physical world in terms of the ideals that capture the real essence that is dimly reflected in physical existence.
		Mathematical captures the mathematical properties of the ideal circle as an abstract structure.
		In particular it is not true on the surface of a sphere which is the geometry we inhabit.
	www.mtnmath.com /whatth/node7.html (464 words)

	Alpaca Books from Northwest Alpacas
		This is because many primitive and unimproved alpacas found in the U.S. were imported in the mid 1980's from Chile.
		The primitive or unimproved alpacas which were originally imported came from small Indian herds, both Quechua and Aymara: 85 to 95 percent of all the world's alpacas reside in these Indian herds.
		Alpacas closer to the ideal are found in the Peruvian alpaca co-ops, such as Rural Allianza and Sollocota.
	www.alpacas.com /Books/IdealAlpaca/Introduction.aspx (1200 words)

	Primitive Enterprises and Paul Eklund
		The Primitive Racing Impreza USX was built in late 1998 and took the ProRally series by storm starting with an impressive finish at the 1999 Rim of the World event (6th overall).
		Primitive Racing will be testing some new ice tires from Cooper Tire for use in the 2004 Alcan Winter Rally at this brisk TSD event.
		The Primitive team has begun a program to lighten their rally cars, rebuild all suspension units, replace under-car shielding, and tire test in order to be ready for the upcoming 2003 Rally season.
	www.writerguy.com /primitive/primitive.htm (2604 words)

	History of the Origins of Christianity. Book II. The Apostles. \| Christian Classics Ethereal Library
		That the author of the Acts, to whom we are indebted for the picture of this primitive Christianity at Jerusalem, has laid on his colours a little too thickly, and, in particular, exaggerated the community of goods which obtained in the sect, is certainly possible.
		The author of the Acts is the same as the author of the third gospel, who, in his life of Jesus, had the habit of adapting his facts to suit his theories, and with whom a tendency to the doctrine of ebonism, that is to say, of absolute poverty, is very perceptible.
		The whole symbol of the primitive church might be embraced in one line: “Jesus is the Messiah, the Son of God.” This belief rested upon a peremptory argument—the fact of the resurrection, of which the disciples claimed to be witnesses.
	www.ccel.org /ccel/renan/apostles.viii.html?scrBook=Jas&scrCh=5&scrV=13 (4431 words)

	bible.org: ISBE (Site not responding. Last check: 2007-09-30)
		She is a rational and accountable creature, as Adam is. In primitive intellectual and moral transactions she has share on equality with Adam, and is equally involved in their results.
		But Adam does not escape retribution for sin, and it may be questioned whether its burden did not fall hardest on him (Gen 3:18,19), for motherhood has its joy as well as its pain, in the companionship of new-born child-life; but the wrestler for subsistence from a reluctant earth must bear his hardship alone.
		That the children of Israel had a tough grasp on the primitive monogamic ideal is not only apparent in all their history, but it comes out clear in what they held as history before their own began.
	www.bible.org /isbe.asp?id=3364 (2882 words)

	E. Belfort Bax: Religion v. Ethics (1901) (Site not responding. Last check: 2007-09-30)
		But this was merely in consonance with the theory of the universe or of the nature of things proper to the animistic phase of mind belonging to primitive man. Its end as religion was the glory of the kinship society.
		Similarly, the so-called universal or ethical religions, whose ideal was primarily individualistic (cf., Christianity) are bound up with the more refined and developed forms of animism called theology, because this also represents the way of looking at things peculiar to that stage of human development.
		Lastly, we, while rejecting the individualist ideal of the great religions and returning to the social ideal of primitive man transformed and universalised as modern international scientific Socialism, have finally left animism behind us, whether in its earlier crude or its later refined form.
	www.marxists.org /archive/bax/1901/09/letter-21-9.htm (345 words)

	Bresenham’s Method
		Bresenham’s Method is a method for developing graphics primitive algorithms that use only whole number mathematics.
		The goal of drawing a graphics primitive on a raster device is to light up the pixels that are closest the ideal shape of the primitive.
		When implementing algorithms based on this method it is necessary to pay attention to the slope of the primitive that is being drawn.
	pages.prodigy.net /j_alan/hitech/graphics/04_04BresMeth.html (1590 words)

	A Commentary on the Rule of the Community of the Resurrection
		The chief ideal of the Community is a renewal of the first fervour of the apostolic church in the primitive era.
		In offering the Eucharist, our ideal is primitive rather than medieval; for we regard ourselves as one body uniting in a common act of eucharistic worship, rather than as a number of priests each of whom will aim at saying his mass daily.
		An ideal however that has such warrants as these was bound to work powerfully in Christian life; and in fact it is probable that the value of celibacy in itself has been over-estimated rather than under-estimated in the system of the Church.
	anglicanhistory.org /frere/crcommentary.html (6650 words)

	Springer Online Reference Works
		Analogously, by using left primitive rings one can define left primitive ideals.
		of all primitive ideals of a ring, endowed with some topology, is useful in the study of various classes of rings.
		The set of all primitive ideals of a ring endowed with this topology is called the structure space of this ring.
	eom.springer.de /p/p074580.htm (91 words)

	David Vogan's References
		Joseph, On the classification of primitive ideals in the enveloping algebra of a semisimple Lie algebra, Lie Group Representations I, R. Herb, R. Lipsman and J. Rosenberg, eds.
		Joseph, On the associated variety of a primitive ideal J. Algebra 93 (1985), 509-523.
		Joseph, The primitive spectrum of an enveloping algebra, Orbites Unipotentes et Representations III.
	www-math.mit.edu /~dav/ref.html (4375 words)

	Singular Manual: primitive
		If the ground field k has only a few elements it may happen that no linear combination of a[1],...,a[n] is a primitive element.
		LIB "primitiv.lib"; ring exring=0,(x,y),dp; ideal i=x2+1,y2-x; // compute Q(i,i^(1/2))=:L ideal j=primitive(i); j[1]; // L=Q(a) with a=(-1)^(1/4) ==> y4+1 j[2]; // i=a^2 ==> y2 j[3]; // i^(1/2)=a ==> y // the 2nd element was already primitive!
		j=primitive(ideal(x2-2,y2-3)); // compute Q(sqrt(2),sqrt(3)) j[1]; ==> y4-10y2+1 j[2]; ==> 1/2y3-9/2y j[3]; ==> -1/2y3+11/2y // no element was primitive -- the calculation of primitive elements // is based on a random choice.
	www.msri.org /about/computing/docs/singular/sing_599.htm (184 words)

	Image Generation and Shape Recognition Toolkit by UW ISL
		Each primitive is mildly constrained so that its digital image bears a reasonable resemblance to the ideal continuous primitive.
		The different primitives are randomly selected, generated and combined to form the different shape models.
		Model and image sizes, overlap between primitives in a model, range for the number of primitives in a model, range for the number of models in an image, range for the scales of models in an image, and noise level are some of the parameters that are allowed to be changed in the code.
	www.ee.washington.edu /research/isl/IAPR/ICPR00/shape_recognition/shape_recognition.html (736 words)

	March to Zion :: Articles :: PB Hurricane relief Update #1
		Due to the late night arrival and dangerous conditions without, the delivery to the Ideal Primitive Baptist church meeting house was delayed to the following morning.
		Another delivery from the Ideal meeting house was made to the Mobile, AL area on Sunday, September 4, 2005, which was much needed.
		The contents of this trailer were off-loaded in a vacant parking lot across the street from Ideal Primitive Baptist Church, and distributed by deacons and members of Ideal church.
	www.marchtozion.com /index.php/news/618 (635 words)

	ALL COUNTEREXAMPLES (Site not responding. Last check: 2007-09-30)
		A nonclosed ideal that is not self-adjoint in a commutative C*-algebra.
		A closed ideal I of a commutative C-algebra A and a closed ideal* J of I such that J isn't an ideal of A. CW11.dvi
		A primitive C*-algebra A acting on a Hilbert space H such that the intersection of A and A' is {0}.
	web.um.ac.ir /~moslehian/cfa/ALL.HTM (1368 words)

	Variable Transformer
		The ideal transformer itself, if it had a means of adjusting the turns ratio dynamically, is useful both for investigating and simulating designs where such a device may be used.
		Ideal Transformer Model: The ideal transformer model was described previously described as having a symbol as follows.
		The output was left isolated to allow the device to be 'rotated', and for generality.
	www.beigebag.com /case_xfrmer_variable.htm (517 words)

	More on The Structure of Completely Reducible Rings
		is a finite direct sum of minimal two-sided ideals which are simple rings.
		is a two-sided ideal and therefore it is zero.
		6 A primitive left-artinian ring is isomorphic to a ring of matrices over a division ring.
	www.wisdom.weizmann.ac.il /~nadavs/reps/node8.html (302 words)

	Carmelnet: Titus Brandsma - Decline and reforms
		What is remarkable is that the Order had so much vitality to restore the primitive ideal after a period of decline.
		Decadence, moreover; is never such that there are not some convents where the primitive rule is kept intact.
		At the beginning of the 15th century when the Popes mitigated the rule, a group of Italian convents in the region of Mantua remained faithful to the primitive spirit, and approved moreover by Papal authority, were organized into a congregation which would flourish greatly.
	carmelnet.org /titus/html/lect12.htm (425 words)

	Prayer-meetings: Shall the prayer-meeting be hybridized?
		If a mine didn't pay with primitive pick and shovel, make it half mine and half ice-plant, or one-fourth mine and three-fourths summer resort; that might solve the problem of getting the most riches out of the mine.
		The prayer-meeting must keep to the primitive ideal, but not the primitive methods.
		The belief that primitive, pick-and-shovel methods are to blame for much of the falling off in interest in the prayer-meeting, stimulates the following rudimentary suggestions, which will be the basis of this book, and will be developed in detail in subsequent chapters.
	www.abcog.org /cowan1.htm (773 words)

	Linville Gorge - The Wilderness Experience
		As a visitor to the wilderness, you should be aware that you are entering a primitive environment where you will be faced with the challenge of being entirely self-sufficient for whatever time you decide to remain there.
		There will be no shelters, campgrounds, water spigots, restrooms, or detailed trail signs.
		Primitive facilities if critical to the protection of the resources
	www.ncnatural.com /Resources/Adventure/Gorge/Wilderness.html (680 words)

	Structure of Semi-primitive Artinian Rings
		1 A ring is primitive if it has a faithful irreducible representation.
		and hence a nilpotent ideal is a nil ideal.
		is a nilpotent ideal which contains all nil (hence nilpotent) ideals.
	www.wisdom.weizmann.ac.il /~nadavs/reps/node7.html (110 words)

	Morphy Lake (Site not responding. Last check: 2007-09-30)
		Sitting pretty at 8,000 feet among ponderosa pines and surrounded by mountains, Morphy Lake is the perfect place to get awat from it all, catch a few fish and enjoy the scenery.
		The park has plenty of camping and picknicking sites, and is ideal for primitive camping.
		The lake is stocked with trout and is a great place to launch a canoe or kayak.
	www.emnrd.state.nm.us /emnrd/parks/MorphyLake.htm (212 words)

	Little Rock District - Clearwater Lake
		We have many areas that are ideal for primitive camping.
		You must obtain a permit prior to any primitive camping at Clearwater Lake.
		This permit may be used to locate your camp group in the event of an emergency.
	www.swl.usace.army.mil /parks/clearwater/camping.htm (121 words)

	Girl Scouts of Rhode Island: Camp - Spotlight on 6 Properties
		It is known for its oak and pine woodlands, medium-sized pond, a one-mile long hiking trail and many brilliant flowers and plants marked along the way.
		This camp is ideal for primitive camping and has a large field for games and sports.
		Camp Promising Acres is ideal for primitive camping.
	www.gsri.org /matriarch/switch.asp_Q_pageid_E_72 (1044 words)

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