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	Encyclopedia: Local ring (Site not responding. Last check: 2007-10-21)
		A ring R is local if it has one (and therefore all) of the following equivalent properties: In ring theory, a branch of abstract algebra, a ring is an algebraic structure in which addition and multiplication are defined and have similar properties to those familiar from the integers.
		In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law.
		The Jacobson radical m of a local ring R (which is equal to the unique left maximal ideal and also to the unique right maximal ideal) consists precisely of the non-units of the ring; furthermore it is the unique two-sided maximal ideal of R.
	www.nationmaster.com /encyclopedia/Local-ring (2982 words)

	PlanetMath: local ring
		The name comes from the fact that these rings are important in the study of the local behavior of varieties and manifolds: the ring of function germs at a point is always local.
		is invertible in the ring of germs at
		This is version 9 of local ring, born on 2002-05-02, modified 2003-12-08.
	planetmath.org /encyclopedia/LocalRing.html (380 words)

	Regular local ring - Wikipedia, the free encyclopedia
		In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is exactly the same as its Krull dimension.
		Regular local rings were originally defined by Wolfgang Krull, but they first became prominent in the work of Oscar Zariski, who showed that geometrically, a regular local ring corresponds to a smooth point on an algebraic variety.
		If p is an ordinary prime number, the ring of p-adic integers is an example of a discrete valuation ring, and consequently a regular local ring, which does not contain a field.
	en.wikipedia.org /wiki/Regular_local_ring (704 words)

	Token ring - Wikipedia, the free encyclopedia
		Stations on a Token-Ring LAN are logically organized in a ring topology with data being transmitted sequentially from one ring station to the next with a control token circulating around the ring controlling access.
		Token ring networks had significantly superior performance and reliability compared to early shared-media implementations of Ethernet (IEEE 802.3), and were widely adopted as a higher-performance alternative to shared-media Ethernet.
		A data token ring frame is an expanded version of the token frame that is used by stations to transmit medium access control (MAC) management frames or data frames from upper layer protocols and applications.
	en.wikipedia.org /wiki/Token_ring (1368 words)

	Local ring: Definition and Links by Encyclopedian.com - All about Local ring (Site not responding. Last check: 2007-10-21)
		In this case the ring also has a unique maximal right ideal, which is a two-sided maximal ideal.
		Other examples of commutative local rings include the ring of rational numbers with odd denominator, and more generally the localization[?] of any commutative ring at a prime ideal.
		Non-commutative local rings arise naturally as endomorphism rings in the study of direct sum decompositions of modules over commutative rings.
	www.encyclopedian.com /lo/Local-ring.html (429 words)

	Local ring (Site not responding. Last check: 2007-10-21)
		In abstract algebra, local rings are certain rings that are comparatively simple and serve to describethe local behavior of functions defined on varieties or manifolds.
		In the case of commutative rings one does not have todistinguish between left, right and two-sided ideals: a commutative ring is local if and only if it has a unique maximalideal.
		The Jacobson radical m of a local ring R(which is equal to the unique left maximal ideal and also to the unique right maximal ideal) consists precisely of the non-unitsof the ring; furthermore it is the unique two-sided maximal ideal of R.
	www.therfcc.org /local-ring-206649.html (1005 words)

	Why a Ring?
		Since there are already several competing local network designs that use contention-controlled broadcast on passive coaxial cable rather than a repeater ring, we are often asked why one should bother to develop an alternative approach--the contention-controlled broadcast technology is field proven, its properties are well understood and adequate for the application.
		To avoid designating some one ring node as special (and thereby making ring operation depend on that node's continued good health) some algorithm is required whereby all active repeaters can quickly and simply agree upon the need for initialization and recovery, and not fall all over one another trying to accomplish it.
		In a token-controlled ring, an error may destroy the token at the worst possible time, or when a station nearing a deadline finally receives the token the message it sends may be damaged by an error, and retransmission may be needed.
	web.mit.edu /Saltzer/www/publications/whyring/whyring.html (5316 words)

	Hampton Union Local News: Ring's resignation accepted by Board (Site not responding. Last check: 2007-10-21)
		Ring, 61, has been on paid administrative leave from the school since Dec. 3, 2002 when he was arrested and charged with shoplifting by Exeter Police.
		Ring signed a letter of resignation drafted by Elwell that releases the school district of all contractual and financial obligations.
		The unanimous School Board vote came five days after Ring allegedly entered the home of a 10-year-old student and his sister when their parents were not there, in order to reprimand him for an alleged scuffle on the school bus that afternoon, according to the parents.
	www.seacoastonline.com /2003news/hampton/03072003/news/16504.htm (718 words)

	Local ring -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Every ring of (Click link for more info and facts about formal power series) formal power series over a field (even in several variables) is local; the maximal ideal consists of those power series without constant term.
		Given a field K, we may look for local rings in it on the assumption that it is a (Click link for more info and facts about function field) function field.
		The (Click link for more info and facts about Jacobson radical) Jacobson radical m of a local ring R (which is equal to the unique left maximal ideal and also to the unique right maximal ideal) consists precisely of the non-units of the ring; furthermore it is the unique two-sided maximal ideal of R.
	www.absoluteastronomy.com /encyclopedia/l/lo/local_ring.htm (1383 words)

	Maximum Press : Home : AS/400 Encyclopedia : Token-Ring Local Area Networks (Site not responding. Last check: 2007-10-21)
		The token-ring is an IBM-developed local area network able to move information at speeds of either 4 or 16 Mbps, depending on the version.
		The protocol used by the token-ring local area network is called the token passing protocol (see "Token-Passing Protocol").
		With this protocol, "packets" of information are passed around the ring from node to node in a continuous circle.
	www.maxpress.com /encyclopedia/tokenrin.htm (306 words)

	Boston.com / News / Local / Conn. / Ring lost on beach returned to owner 43 years later (Site not responding. Last check: 2007-10-21)
		Taylor's parents gave her the ring in 1956 when she graduated from Bishop O'Dowd High School in Oakland, Calif. It had the name of her school and "Corpus Christi" engraved on the outside, and the initials for Wilhemina Mae Lavato on the inside.
		When Taylor lost the ring in 1961, she was living in Groton with her husband, an officer on the USS Patrick Henry, and three young children.
		When Vassallo found the ring about 100 feet from the water, all she had to go on were the engravings.
	www.boston.com /news/local/connecticut/articles/2004/08/09/ring_lost_on_beach_returned_to_owner_43_years_later (472 words)

	Local article - Local moved Wiktionary expanded guidelines dictionary.com local ring - What-Means.com (Site not responding. Last check: 2007-10-21)
		Local article - Local moved Wiktionary expanded guidelines dictionary.com local ring - What-Means.com
		Of or relating to a city, town, or district rather than a larger area: state and local government.
		A local chapter or branch of an organization, especially of a labor union.
	www.what-means.com /encyclopedia/Local (184 words)

	Local ring
		In abstract algebra, a local ring is a ring which has a unique maximal left ideal.
		Every local ring also has a unique maximal right ideal, and this right ideal is equal to the unique maximal left ideal (and equal to the ring's Jacobson radical) and hence a two-sided maximal ideal.
		The kind of example that motivates the definition is the commutative ring R of real-valued continuous functions defined on some interval around 0 of the real line.
	www.ukpedia.com /l/local-ring.html (524 words)

	Encyclopedia: Regular local ring (Site not responding. Last check: 2007-10-21)
		In abstract algebra, a polynomial ring is the set of polynomials in one or more variables with coefficients in a ring.
		Categories: Algebraic geometry In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers.
		In mathematics, a discrete valuation ring (DVR) is a particular kind of commutative ring that is a local ring, which satisfies conditions that in algebraic geometry come from non-singularity of a point on an algebraic curve.
	www.nationmaster.com /encyclopedia/Regular-local-ring (1257 words)

	Element Constructions and Conversions (Site not responding. Last check: 2007-10-21)
		Local ring elements are implemented using a balanced mod representation.
		To create an element of a local field not lying in the local ring, constructors are provided that create an element coercible into the ring, and which increase or decrease this element's valuation in the field.
		Given a local ring or field L, return a random element of L, which must be a quotient ring or bounded precision ring.
	magma.maths.usyd.edu.au /magma/htmlhelp/text750.htm (1131 words)

	Operations on Elements
		Two elements of a local ring or field are only regarded as equal, if their valuations, precisions and digits are identical.
		Return the precision to which the local element x is known, that is, the number of terms or digits of x which are known, starting from the term of valuation zero for ring elements and from the term of lowest valuation for field elements.
		For ring elements x, the answer lies in the ring (and not its field of fractions) only if the valuation of x - 1 is greater than or equal to the ramification degree of the ring divided by the prime.
	www.math.niu.edu /help/math/magmahelp/text727.html (1664 words)

	Regular local ring (Site not responding. Last check: 2007-10-21)
		Geometrically, a regular local ring corresponds to a smooth point on an algebraic variety.
		Thus if one forms the ring of germs of holomorphic functions at a smooth point on an algebraic variety defined in several complex variables, that will be a regular local ring.
		If p is an ordinary prime number, the ring of p-adic integers is an example of a discrete valuation ring which does not contain a field.
	www.sciencedaily.com /encyclopedia/regular_local_ring (313 words)

	Boston.com / News / Local / Elizabeth Ring, 85, Haverhill secretary
		Elizabeth B. (Burchstead) Ring of Haverhill, a retired secretary, died Jan. 5 at her home.
		Ring was a member of St. James Parish in Haverhill, the Greater Haverhill Arts Association, the Disabled American Veterans Auxiliary, and the Animal Rescue League of Boston.
		She leaves her husband, William Albert Ring of Haverhill; one sister, Jane B. Theriault of Haverhill; five nieces; and two nephews.
	www.boston.com /news/local/articles/2005/01/13/elizabeth_ring_85_haverhill_secretary (601 words)

	RFC 1469 (rfc1469) - IP Multicast over Token-Ring Local Area Networks
		Addresses supplied to or received from token ring interfaces are usually laid out in memory with the bits of each octet in the opposite order from that illustrated, i.e., with bit 0 in the high-order (leftmost) position within the octet.
		If the I/G bit is 1 and the U/L bit is a 1, the address may be either a local administered group address or a functional address.
		Bridges may provide a means to translate between different methods for each physical ring that is being bridged.
	www.faqs.org /rfcs/rfc1469.html (1065 words)

	Local ring - InfoSearchPoint.com (Site not responding. Last check: 2007-10-21)
		The exact same arguments work for the ring of germs of continuous real-valued functions on any topological space at a given point, or the ring of germs of differentiable functions on any differentiable manifold at a given point, or the ring of germs of rational functions on any algebraic variety at a given point.
		These examples explain why schemes, the generalizations of varieties, are defined as special locally ringed spaces.
		) is local with maximal ideal consisting of the classes of polynomials with non-zero constant term.
	www.infosearchpoint.com /display/Local_ring (1012 words)

	Magic, King Magic Ring, IBM Ring 94
		Ring #94 is the oldest Ring in the State of Maryland and was chartered on April 25, 1949.
		In 1972, with the enthusiasm of a couple of members, the Ring was rechartered and has been active since, still holding monthly meetings and an annual banquet every June.
		This was the first time the Ring undertook a project of this magnitude and it was a tremendous success.
	www.kingmagicring.com (749 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		On the embedding of a commutative ring in a local ring
		This leads naturally to an examination of conditions in order that a quasilocal ring (R,m) be dominated by a local ring.
		We prove several results concerning domination of a quasilocal ring by a local ring including the result that a zero-dimensional quasilocal ring that is embeddable in a Noetherian ring is dominated by an Artinian local ring.
	www.math.fsu.edu /~aluffi/archive/paper71.abs.html (112 words)

	Boston.com / News / Local / A ring and a prayer
		Maberry, a 65-year-old retired nurse and an L Street Brownie, brought it home, cleaned it in the dishwasher, and took a closer look: It was a Class of 1978 ring with the words ''Don Bosco Tech." Carved into it was a bear, the mascot of the former South Boston Catholic school.
		The jury foreman, 48-year-old Kevin Kennedy, told her that he had an idea: The man he married in June shortly after Massachusetts legalized gay marriage graduated from Don Bosco in 1978, and he might have a yearbook.
		He said the ring probably lay buried on the beach all that time and was exposed after a storm or big waves.
	www.boston.com /news/local/articles/2005/01/24/a_ring_and_a_prayer (631 words)

	PlanetMath: regular local ring
		elements, so the maximal ideals of regular local rings have a minimal number of generators.
		Cross-references: generators, minimal number, Krull's principal ideal theorem, projection, images, generate, Nakayama's lemma, Krull dimension, vector space, maximal ideal, local ring
		This is version 3 of regular local ring, born on 2002-12-27, modified 2004-04-23.
	planetmath.org /encyclopedia/RegularLocalRing.html (114 words)

	Clearing up the market cycle... best Regular Local Ring (Site not responding. Last check: 2007-10-21)
		Regular Local Ring -- from MathWorld Regular Local Ring -- from MathWorld A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently...
		In commutative algebra, a regular local ring is a Noetherian local ring having the property that...
		Regular Ring -- from MathWorld Regular Ring -- from MathWorld A regular ring in the sense of commutative algebra is a commutative unit ring such that all its localizations at prime ideals are regular local rings.
	ascot.pl /th/Fourier5/Regular-Local-Ring.htm (917 words)

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