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Topic: Group ring

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	Group ring - Wikipedia, the free encyclopedia
		In mathematics, the group ring is an algebraic construction that associates to a group G and a commutative ring with unity R an R-algebra R[G] (or sometimes just RG) such that the multiplication in R[G] is induced by the multiplication in G.
		When G is a finite abelian group, the group ring is commutative, and its structure easy to express in terms of roots of unity.
		An example of a group ring of an infinite group is the ring of Laurent polynomials: this is exactly the group ring of the infinite cyclic group Z.
	en.wikipedia.org /wiki/Group_ring (403 words)

	Ring (mathematics) - Wikipedia, the free encyclopedia
		Rings that also satisfy commutativity for multiplication (such as the ring of integers) are called commutative rings.
		A ring (in the categorical sense) is commutative iff it is equal to its opposite ring.
		The split-complex plane D is a ring useful in modern physics and is a subring of the tessarines.
	en.wikipedia.org /wiki/Ring_(mathematics) (1102 words)

	PlanetMath: group
		Groups often arise as the symmetry groups of other mathematical objects; the study of such situations uses group actions.
		See Also: subgroup, cyclic group, simple group, symmetric group, free group, ring, field, group homomorphism, Lagrange's theorem, identity element, proper subgroup, groupoid, fundamental group, topological group, Lie group, Proof: The orbit of any element of a group is a subgroup, locally cyclic group, existence of Hilbert class field, abelian group,
		This is version 16 of group, born on 2001-08-29, modified 2005-03-14.
	planetmath.org /encyclopedia/Group.html (277 words)

	Group ring -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		When G is a finite (A group that satisfies the commutative law) abelian group, the group ring is commutative, and its structure easy to express in terms of (Click link for more info and facts about roots of unity) roots of unity.
		An example of a group ring of an infinite group is the ring of (Click link for more info and facts about Laurent polynomial) Laurent polynomials: this is exactly the group ring of the (Click link for more info and facts about infinite cyclic group) infinite cyclic group Z.
		There is a neat characterisation from (Click link for more info and facts about category theory) category theory of the group ring construction as the (Click link for more info and facts about left adjoint) left adjoint to the functor taking an associative R-algebra with one to its group of units.
	www.absoluteastronomy.com /encyclopedia/g/gr/group_ring.htm (339 words)

	PlanetMath: group ring
		is defined to be the ring whose additive group is the abelian group of formal integer linear combinations of elements of
		whose additive group is the abelian group of formal
		This is version 4 of group ring, born on 2002-01-23, modified 2002-11-06.
	planetmath.org /encyclopedia/GroupRing.html (127 words)

	Group ring (Site not responding. Last check: 2007-10-08)
		In mathematical representation theory, thegroup ring or group algebra is an abstract algebra construction, that allows representations of a group G, over a field K, to be treated as modules.
		The ring constructed (notation K[G], or sometimes just KG) can be described as the vector space over K with basis the elements g of G, and ring multiplication the group operation in Gextended by bilinearity to the whole space.
		An example of a group ring of an infinite group is the ring of Laurent polynomials : this is exactly the group ring of an infinite cyclic group.
	www.therfcc.org /group-ring-210852.html (556 words)

	Group ring (Site not responding. Last check: 2007-10-08)
		In mathematical representation theory the group ring or group algebra is an abstract algebra construction that allows representations of a group G over a field K to be treated as modules.
		When G is a finite abelian group the group ring is commutative and structure easy to express in terms of roots of unity.
		An example of a group ring of infinite group is the ring of Laurent polynomials : this is exactly the group ring an infinite cyclic group.
	www.freeglossary.com /Group_ring (857 words)

	PlanetMath: orthogonal idempotents of the group ring
		, the corresponding orthogonal idempotent of the group ring
		"orthogonal idempotents of the group ring" is owned by mathcam.
		This is version 6 of orthogonal idempotents of the group ring, born on 2004-02-27, modified 2005-05-15.
	www.planetmath.org /encyclopedia/OrthogonalIdempotentsOfTheGroupRing.html (86 words)

	Ring (mathematics) - Open Encyclopedia (Site not responding. Last check: 2007-10-08)
		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.
		If a subset S of a ring (R,+,) together with the operations + and restricted on S is itself a ring, and the identity element 1 of R is contained in S, then S is called a subring of (R,+,*).
		The centre of a ring R is the set of elements of R that commute with every element of R; that is, c lies in the centre if cr=rc for every r in R.
	open-encyclopedia.com /Ring_(mathematics) (1045 words)

	20: Group Theory and Generalizations
		Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way.
		Groups acting on topological spaces are the basis of equivariant topology and homotopy theory in Algebraic Topology.
		Nielsen's theorem: subgroups of free groups are free.
	www.math.niu.edu /~rusin/known-math/index/20-XX.html (2774 words)

	Group of Ring (Site not responding. Last check: 2007-10-08)
		Nine rings were the gifted to competition of the person, especially other craving power.
		Strength and the will which in these rings control each competition for the sake of it was divided.
		With the land of the Mordor of the fire of destiny of the mount, as for the Sauron dark main thing the master ring which controls other everything with secret was made.
	www.expage.com /fwengrishfotr1 (536 words)

	Group ring target - Patent 4189146
		Another object is to provide a group ring in which the ring members are simply made of a flat material, adaptable to be pierced by arrows, and which can be readily secured to a side of a bale of hay, so that the target itself does not require any padding construction upon its rear.
		The inner ring 12 is provided with a pair of rearwardly extending pins 18, extending rearwardly from its rear side 19, and which are used for piercing into the bale of hay, in order to support the inner ring therefrom.
		The outer ring, with its hooks 15 is, of course, placed against the bale of hay in only one way, whereas the inner ring can be selectively rotated in any direction, so that any one of the numerals upon the inner ring can be aligned with the numerals of the outer ring.
	www.freepatentsonline.com /4189146.html (1026 words)

	Encyclopedia: Ring (algebra) (Site not responding. Last check: 2007-10-08)
		A ring is an abelian group (R, +), together with a second binary operation * such that for all a, b and c in R,
		In this encyclopedia, associativity and the existence of a multiplicative identity are taken to be part of the definition of a ring.)
		An element a in a ring is called a unit if it is invertible with respect to multiplication, i.e., if there is an element b in the ring such that
	www.nationmaster.com /encyclopedia/ring-(algebra) (1073 words)

	ABSTRACT ALGEBRA ON LINE: Modules (part 2)
		Let R be a ring, and let G be a group.
		The group ring RG is defined to be a free left R-module with the elements of G as a basis.
		The crucial property of a group ring is that it converts group homomorphisms from G into the group of units of a ring into ring homomorphisms.
	www.math.niu.edu /~beachy/aaol/modules2.html (1490 words)

	Professor Lomonaco: Metacyclic Error-Correcting Codes (Site not responding. Last check: 2007-10-08)
		Error-correcting codes which are ideals in group rings where the underlying group is metacylic and non-abelian are examined.
		Group rings that are semi-simple, i.e., where the characteristic of the field does not divide the order of the group, are considered.
		In all cases, the field of the group ring is of characteristic
	www.cs.umbc.edu /~lomonaco/Abstract2.html (189 words)

	The Ring - Air Group 4
		One group of 20 Douglas Dauntless dive-bombers with a fighter escort was directed to attack German shipping near the Norwegian port of Bodø.
		The second strike group, consisting of 9 Grumman Avenger torpedo-bombers with fighter cover, was sent to the fjords near Sandnessjøen, Norway.
		In 1990, a group of amateur scuba divers, who were also Norwegian Air Force pilots, discovered the wreckage of a US Navy aircraft in the North Atlantic, just outside the harbor of Bodø.
	www.airgroup4.com /ring.htm (1552 words)

	RFC 1513 (rfc1513) - Token Ring Extensions to the Remote Network Monitorin (Site not responding. Last check: 2007-10-08)
		Network Working Group S. Waldbusser Request for Comments: 1513 Carnegie Mellon University Updates: 1271 September 1993 Token Ring Extensions to the Remote Network Monitoring MIB Status of this Memo This RFC specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements.
		Some of those functional groups, the statistics and the history groups, have a view of the data-link layer that is specific to the media type and require specific objects to be defined for each media type.
		Guidelines for implementing RFC1271 objects on a Token Ring network Wherever a MacAddress is to be used in this MIB the source routing bit is stripped off.
	www.faqs.org /rfcs/rfc1513.html (2845 words)

	The RING Alliance
		The Ring is now a known and established network in the field, and has developed an international reputation of excellence.
		The Ring are leading a programme of work focusing on the European Union's impacts on the rest of the world, and the ways in which these could be made more sustainable and accountable.
		In 2003, the Ring was invited by the Secretariat of the United Nations Global Compact to prepare a think-piece with suggestions on ways to strengthen the development dimension of the Global Compact.
	www.ring-alliance.org (1864 words)

	'No sex' message doesn't ring true - World - www.theage.com.au
		Silver Ring Thing, the invention of Pennsylvania-based evangelist Denny Pattyn, is a youth movement with the aim of encouraging young people to swear off sex before marriage.
		Members denote their unavailability for furtive adolescent gropings by wearing a special $A26 silver ring which, if all goes well, will be handed to their eventual spouses as a symbol of commitment and forbearance.
		The group also does a booming trade in merchandise (T-shirts, bumper stickers that declare "I'm Waiting") and is one of the recipients of the Bush Administration's $US120 million annual funding to teen abstinence groups.
	www.theage.com.au /articles/2004/06/25/1088144972916.html (539 words)

	Sauk County,WI Freecycling Group Ring Network
		The Sauk County Freecycling Group Ring Network has open membership to anyone in the Sauk County, Wisconsin area wanting to start Freecycling with other members within Sauk County, WI Freecycling Group Ring Network.
		Freecycling group of your city or town to join the Freecycling group of your city or town along with joining the Sauk County, WI Freecycling Group Ring Network.
		The Sauk County, WI Freecycling Group Ring Network is a great place to find almost anything you might spend your hard earned money on for in the stores like computers, furniture, clothing, electronics etc where on Freecycling Network of Sauk County, WI you may be able to find it and get it for FREE.
	webpages.charter.net /techdoctors (260 words)

	Meet a wonderful group of Ring-tailed Lemurs
		For obvious reasons they were named for their highly contrasting Black and White ringed tails.
		They are found on the South and Southwestern part of the island of Madagascar and live in large groups or "Troops" (often exceeding 20 individuals).
		I could start babbling on and on about the different infant developments both socially in the group and physically as it grows; but I think I will wait to put that in a subsequent Sanctuary Chronicle.
	www.tigerhomes.org /animal/chrondex/group-ring-tailed-lemurs.cfm (914 words)

	Counter examples, Group and Ring theory - Science Forums and Debate (Site not responding. Last check: 2007-10-08)
		Are there famous groups that one needs to know in order to be able to construct counter examples to famous theorems in group and ring theory?
		S_3 is the smallest non-abelian group, that is why it is used - it will often be the simplest counter example.
		Every group of order p^2 is abelian, hence S_3 is the first possible non-abelian group.
	www.scienceforums.net /forums/showthread.php?t=7749 (322 words)

	The YHA Group Ring
		The purpose of this ring is to assist viewers to locate a YHA group near them as well as to see what other groups are getting up to.
		If you are visiting the YHA Group Ring, most sites will have the YHA Group Ring logo near the bottom of the home page, a few may not.
		The YHA Group Ring logo is the standard that will be used by all members of the ring.
	yhagroup.org.uk /ring (613 words)

	Ring Company : Group Discounts (Site not responding. Last check: 2007-10-08)
		Get a group of your friends to order together and enjoy group discount pricing.
		By processing a group order, we cut down on our production costs and pass on these savings to you.
		Get a group of friends or schoolmates to agree to place your orders together.
	www.ringcompany.com /discount.html (130 words)

	Silver Ring group faces ACLU suit - PittsburghLIVE.com
		The group is based at Christ Church at Grove Farm, a nondenominational Protestant church.
		The Silver Ring Thing is an offshoot of the John Guest Evangelistic Team, a Christian ministry based at Christ Church.
		The lawsuit also complains that the silver rings sold to youths who take the abstinence pledge are inscribed with a reference to a biblical verse which says, "God wants you to be holy, so you should keep clear of all sexual sin.
	www.pittsburghlive.com /x/tribune-review/trib/pittsburgh/s_334951.html (665 words)

	IEEE 802.17 RPR Working Group Home Page
		The working group email reflector is open to any interested participant or observer.
		The IEEE 802.17 Resilient Packet Ring Working Group (RPRWG) develops standards to support the development and deployment of Resilient Packet Ring networks in Local, Metropolitan, and Wide Area Networks for resilient and efficient transfer of data packets at rates scalable to many gigabits per second.
		These rings are currently using protocols that are neither optimized nor scalable to the demands of packet networks, including speed of deployment, bandwidth allocation and throughput, resiliency to faults, and reduced equipment and operational costs.
	grouper.ieee.org /groups/802/17 (190 words)

	The group ring of SL_2(2^f) over 2-adic integers. (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		The group ring RG is calculated nearly up to Morita equivalence.
		1991 Mathematics Subject Classification: 20C05, 20C11 1 Introduction The group G = SL 2 (p f) of all 2\Theta2-matrices over the field k with p f elements is one of the simplest examples of a nonabelian finite group of Lie type.
		2 The group ring of SL (context) - Nebe - 1998
	citeseer.ist.psu.edu /274205.html (383 words)

	BBC NEWS \| UK \| Magazine \| How effective are abstinence pledges?
		Denny Pattyn, the founder of the faith-based abstinence group Silver Ring Thing, is touring the UK and Ireland in the hope of persuading young people on this side of the Atlantic to take the pledge.
		His group is one of hundreds across the US that promote self-restraint rather than sex education.
		The only way to see what effect the pledge has is to compare two groups: one that has been exposed to the Silver Ring people, and one that hasn't.
	news.bbc.co.uk /2/hi/uk_news/magazine/3846687.stm (1011 words)

	TheOneRing.net™ \| Scrapbook \| Group \| 'Ring Around The Simpsons'
		The 2003 'Treehouse of Terror' Simpsons comic has this LOTR inspired story called 'Ring Around the Simpsons'.
		It seems the family is transported to Middle-earth and become part of the Fellowship!
		This site is maintained and updated by fans of The Lord of the Rings, and is in no way affiliated with Tolkien Enterprises or the Tolkien Estate.
	www.theonering.net /scrapbook/group/1071 (174 words)

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