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Topic: Primitive ring

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	Jacobson density theorem - Wikipedia, the free encyclopedia
		In mathematics, the Jacobson density theorem in ring theory is an important generalization of the Artin-Wedderburn theorem.
		That this is a division ring is a consequence of Schur's lemma.
		In particular, when the ring is primitive then it is a dense subring of linear transformations of a vector space over a division ring.
	en.wikipedia.org /wiki/Jacobson_density_theorem (178 words)

	Primitive ring - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-21)
		In Abstract algebra, a left primitive ring R is a ring with a faithful simple left module R-module.
		An Artinian ring is primitive if and only if it is simple.
		A commutative ring is primitive if and only if it is a field.
	encyclopedia.worldsearch.com /primitive_ring.htm (176 words)

	Prime ring - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-21)
		In abstract algebra, a ring R is a prime ring if for any two elements a and b of R, if arb = 0 for all r in R, then either a = 0 or b = 0.
		Prime rings can be regarded as a simultaneous generalization of both integral domains and matrix rings over fields.
		In particular, the ring of 2-by-2 integer matrices is a prime ring.
	encyclopedia.worldsearch.com /prime_ring.htm (185 words)

	Common Divisors and Common Multiples (Site not responding. Last check: 2007-10-21)
		The greatest common divisor of polynomials f and g in a univariate polynomial ring P. The coefficient ring of P must be either a field, the ring of integers or a residue class ring with prime modulus, or a polynomial ring over any of these.
		The coefficient ring of P must be either a field, or a residue class ring with prime modulus.
		The least common multiple of polynomials f and g in a univariate polynomial ring P. The coefficient ring of P must be either a field, the ring of integers or a residue class ring with prime modulus.
	www.math.uiuc.edu /Software/magma/text315.html (270 words)

	Eyebrow Ring in TutorGig Encyclopedia (Site not responding. Last check: 2007-10-21)
		Ring is the title of two novels Ring Suzuki novel Ring, a horror novel by Koji Suzuki Ring Baxter novel Ring, a science fiction novel by Michael Baxter disambig..
		A D ring is also a type of metal ring used to join straps, or the ring in a Ring binder.
		The G Ring is one of the rings of Saturn.
	www.tutorgig.com /es/Eyebrow+Ring (997 words)

	Primitive ideal - Wikipedia, the free encyclopedia
		In mathematics, a left primitive ideal in ring theory is the annihilator of a simple left module.
		Note that (despite the name) left and right primitive ideals are always two-sided ideals.
		The quotient of a ring by a primitive ideal is a primitive ring.
	en.wikipedia.org /wiki/Primitive_ideal (70 words)

	primitive \| TutorGig.co.uk - The Tutorial Website (Site not responding. Last check: 2007-10-21)
		primitive can refer to primitive art and Primitivism art primitive biology primitive computer science primitive geometry In the branch of field t..." >Primitive, primitive root may mean either a primitive root modulo n in modular arithmetic, or a primitive...
		Primitive rings..." >Primitive ring, primitive ideal in ring theory is the Annihilator ring theory annihilator of a simple module simple left module mathematics module.
		A right primitive ideal is de..." >Primitive ideal, primitive element can mean in number theory, a primitive root modulo n in field theory mathematics field theory, an element that generates a given field exten..." >Primitive element (More...
	www.tutorgig.co.uk /searchtgig.jsp?keywords=primitive (578 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Corollary.} {For a ring $R$ the following are equivalent: \itemitem{} {\rm (a)} $R$ is simple and left artinian; \itemitem{} {\rm (b)} $R \cong \fatm_n(D)$ for some $n\in \fatn$ and some division ring $D$; \itemitem{} {\rm (c)} $R$ is simple and right artinian.
		Also, deduce from this exercise that there are primitive rings that are not simple.
		Prove that $R$ is semi--primitive iff there is an injective ring homomorphism $\phi:R \longrightarrow \prod_A S_\alpha$ where each $S_\alpha$ is the ring of operators $\End(V_\alpha)$ on a right vector space $V_\alpha$ over a division ring $D_\alpha$, and for each alpha the image $\pi_\alpha\phi(R)$ is dense in $S_\alpha$.
	darkwing.uoregon.edu /~anderson/math648/lecture19.html (1721 words)

	ABSTRACT ALGEBRA ON LINE: Structure of Noncommutative Rings
		The ring R is called a simple ring if (0) is a maximal ideal; it is called a prime ring if (0) is a prime ideal, and a semiprime ring if (0) is a semiprime ideal.
		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)

	PlanetMath: primitive ideal
		is a left (right) primitive ideal if there exists a simple left (right)
		is a left (right) primitive ring if the zero ideal is a left (right) primitive ideal of
		This is version 2 of primitive ideal, born on 2001-11-24, modified 2002-10-25.
	www.planetmath.org /encyclopedia/PrimitiveRing.html (71 words)

	Definition of primitive accumulation of capital
		Musafar]] is considered the father of the modern primitive movement.
		Primitive Lyrics' main domain was live concerts, so they to...
		3:...he quotient of a ring by a primitive ideal is a [[primitive ring]].
	www.wordiq.com /search/primitive+accumulation+of+capital.html (729 words)

	Pip-Berry - Country Style Home Decor
		This country blue pip berry candle ring is a versatile piece that can be used as a candle ring or mini wreath.
		This flag pip berry candle ring is a versatile piece that can be used as a candle ring or mini wreath.
		This navy pip berry candle ring is a versatile piece that can be used as a candle ring or mini wreath.
	countrystylehome.com /Pip-Berry_5.html (413 words)

	[No title]
		Geometric primitive Description, partial or total, of the spatial aspects of an object by means of coordinates and mathematical functions.
		Implicit intersection Two primitives implicitly intersects one each other when their respective interpolation methods applied to its respective lists of coordinates pass two or more times for exactly the same spatial position.
		One primitive intersects implicitly itself when its interpolation method is applied to its list of coordinates and passes two or more times through exactly the same spatial position.
	www.xs4all.nl /~visjpmm/ViaNova/LocationReferences/SpatialG0.doc (615 words)

	Primitive ring - TheBestLinks.com - Jacobson density theorem, Abstract algebra, Field (mathematics), ... (Site not responding. Last check: 2007-10-21)
		Primitive ring - TheBestLinks.com - Jacobson density theorem, Abstract algebra, Field (mathematics), TheBestLinks.com:Find or fix a stub,...
		Jacobson density theorem, Primitive ring, Abstract algebra, Field (mathematics)...
		A commutative ring is primitive if and only if it is a.
	www.thebestlinks.com /Jacobson_density_theorem.html (124 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The primitive ideal of $\g$ collects all the functions whose zero level hypersurfaces pass through $\Sigma$ and are tangent to the regular part $X_{\rm reg}$ of $X$ along $\Sigma \cap X_{\rm reg}$.
		Hence, locally the primitive ideal plays a similar role to the second power of the maximal ideal of the local ring $\O_{\cc ^n, 0}$ in singularity theory.
		The {\it primitive ideal of $\g$} relative to $\h$ is $$\int _{\h}\g:= \{f\in \g\mid \xi (f)\in \g \text{ for any } \xi \in \hder {\h}{\O}\}.$$ \end{Definition} \begin{Remark}\label{geometry}\rm This definition is a generalization of \cite{P1, P2}, and was generalized to higher order relative version in \cite{JS}.
	home.imf.au.dk /esn/preprints/184 (3835 words)

	Greatest Common Divisors (Site not responding. Last check: 2007-10-21)
		The coefficient ring of P must be either a field, the ring of integers, or a polynomial ring over any of these.
		The content of f, that is, the greatest common divisor of the coefficients of f as an element of the coefficient ring.
		The content (the greatest common divisor of the coefficients) of f, as an element of the coefficient ring, as well as the primitive part (f divided by the content) of f.
	www.math.wisc.edu /help/magma/text388.html (171 words)

	elisp : Internals of Kill Ring
		We call the kill ring a "ring" because the functions that move the yank pointer wrap around from the end of the list to the beginning, or vice-versa.
		Rotation of the kill ring is virtual; it does not change the value of `kill-ring'.
		The effect is to rotate the ring so that the newly killed text is at the front.
	techpubs.sgi.com /library/dynaweb_docs/fw/usr/freeware/info_tpl/elisp/elisp_399.html (362 words)

	Ballet-Dance Magazine - University of Washington Chamber Dance Group - Primitive Mysteries, Ring, Beat, Pigs and Fishes ...
		It was great seeing Martha Graham’s early work "Primitive Mysteries" (1931) after a nearly 30 year hiatus off of my radar screen.
		At first blush, it would appear that "Primitive Mysteries" is a quiet dance with lots of “nice” tableaux.
		Graham was never “nice.” In 1931, Graham’s company was only five years old and this work is a solid example of finding her own artistic voice.
	www.ballet-dance.com /200502/articles/UWCDG20050203.html (1104 words)

	Handcrafted Country Angels
		She is carrying a painted tin flag with a little bell and is accented with stick wings, rusty wire halo with rusty tin star and an old red button.
		She is handcrafted from a dark red/navy check brushed homespun and is holding a mini star candle stick with a real primitive taper.
		She is accented with twig wings, a rusty wire halo with a dangling rusty star and an old mop button.
	www.hugsandstitches.com /angels.htm (509 words)

	www.bravenet.com (Site not responding. Last check: 2007-10-21)
		Ring is devoted to the study and admiration (where appropriate) of the British diesel loco.,it's work, duties, preservation and restoration is all in mind.
		This ring is for the devoted cosplayers who set up websites to show their love for cosplaying.
		This ring is for anyone ejoying ham radio and the new mode of Internet linking using the Echo-link program...Any web site with information about Echo-link in general or there echo-link stations are welcome to join.
	www.bravenet.com /search/sitering.php?searchbycategory=1&category=160 (1937 words)

	[No title]
		As derived in MagicSequences.html the smallest and biggest number in a magic square must be on opposite sites of the central number, which means the ring must be of type I, a type II or III ring can't be part of a magic square.
		All primitive SPT's of numbers below 10.000 are in prim_spts.zip the three found rings are also listed in that file, currently I only used those to form rings.
		Interestingly this ring of square numbers has equal summing horizontal triplets also equal summing vertical triplets and equal summing diagonals, further the difference between the horizontal and vertical triplets is equal to the difference between the diagonal sum and both central sums
	home.wanadoo.nl /aaledewinkel/Gen_Magic/PseudoRings.html (748 words)

	Daylight Theory: SMARTS
		The `r' atomic primitive refers to the size of the smallest ring that an atom is in.
		The '@' bond primitive actually took an optional trailing number, which was the minimum number of rings in which the bond must be a member.
		Unfortunately, the ring membership depends on the SSSR (smallest set of smallest rings) which the toolkit perceived for any given molecule, and this property is ambiguous.
	www.daylight.com /dayhtml/doc/theory/theory.smarts.html (2673 words)

	Dynamic recruitment of dynamin for final mitochondrial severance in a primitive red alga -- Nishida et al. 100 (4): ... (Site not responding. Last check: 2007-10-21)
		Changes in the relative circumferences of the PD and MD rings between 3 and 6 h are drawn with broken and solid lines, respectively (23).
		Images of mitochondria and MD rings at each division stage corresponding to A are represented by simple outline drawings and gray images, respectively.
		After FtsZ ring formation, the MD ring appears on the cytosolic side of the outer membrane.
	www.pnas.org /cgi/content/full/100/4/2146 (3971 words)

	Primitive Artists-Pollym and Mary F. ...
		It is presently the leading form of contemporary art, winning acceptance, as more and more museums add it to their permanent collections.
		As one art critic stated, primitive art reveals a "flash of spirit." It brings a smile to your lips or tweaks at your heart.
		Commonly the images are the artists concept of their memories or those of family members, passed down in the form of story telling.
	www.primitiveartists.addr.com (166 words)

	finite fields
		If you have a quotient ring that you know is a finite field, then you can convert it to ring which is known by the system to be a finite field.
		is still recorded as an element of its quotient ring, rather than this finite field.
		Conversely, a given element of the finite field can be transferred back to the quotient ring with lift.
	www.mathematik.uni-ulm.de /help/Macaulay2-0.8.42/523.html (311 words)

	Common Divisors (Site not responding. Last check: 2007-10-21)
		The functions in this section are restricted to multivariate polynomials over a field, over the integers, or any polynomial ring over these.
		The greatest common divisor of f and g in a multivariate polynomial ring P. The coefficient ring of P must be either a field, the ring of integers, or a polynomial ring over any of these.
		The least common multiple of f and g in a multivariate polynomial ring P. The coefficient ring of P must be either a field, the ring of integers, or a polynomial ring over any of these.
	www.math.uiuc.edu /Software/magma/text324.html (160 words)

	elisp : Low-Level Kill Ring
		Low-Level Kill Ring ------------------- These functions and variables provide access to the kill ring at a lower level, but still convenient for use in Lisp programs, because they take care of interaction with window system selections (*note Window System Selections::).
		If N is zero, indicating a request for the latest kill, `current-kill' calls the value of `interprogram-paste-function' (documented below) before consulting the kill ring.
		If the value is a function, `kill-new' and `kill-append' call it with the new first element of the kill ring as an argument.
	techpubs.sgi.com /library/dynaweb_docs/fw/usr/freeware/info_tpl/elisp/elisp_398.html (391 words)

	Folk Art Lane Web Ring
		You will also find primitives, fine country furniture, folk art, personalized grandparent signs, hand painted and crafted needful gatherings.
		Southern Pottery carries the work of more than twenty of the best clay artists with a balance of work in both the southern traditional/historical and contemporary pottery, ceramic forms and face jugs.
		Homespun Primitive, Scrappy, Country, Americana, and Christmas Style Quilts for Home Decor, also potholders, ornies, and candle mats.
	e.webring.com /hub?ring=folkartlanewebri&id=34&hub (1346 words)

	The theta-transfer technique: On Noetherian involution rings and symmetry of primitivity (Site not responding. Last check: 2007-10-21)
		We also study the class of Noetherian involution rings and the problem of symmetry of primitivity.
		In particular, suppose that for every semiprimitive Noetherian involution ring which has exactly two minimal prime ideals both of these satisfy (SP).
		Antihomomorphism, antiautomorphic ring, involution ring, θ-homomorphism, prime ideal, primitive ideal, symmetry of primitivity.
	www.math.hr /glasnik/vol_40/no1_04.html (170 words)

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