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Topic: Radical of a ring

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	Jacobson radical - Wikipedia, the free encyclopedia
		In ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is an ideal of R which contains those elements of R which in a sense are "close to zero".
		The Jacobson radical of the integers is {0}.
		The Jacobson radical of this ring is generated by all the paths in Γ of length ≥ 1.
	en.wikipedia.org /wiki/Jacobson_radical (572 words)

	Ring Theory
		However, axioms for rings are not given by Weber and the axiomatic treatment of commutative rings was not developed until the 1920's in the work of Emmy Noether and Krull.
		In contrast to commutative ring theory, which as we have seen grew from number theory, non-commutative ring theory developed from an idea which, at the time of its discovery, was heralded as a great advance in applied mathematics.
		The greatest early contributor to the theory of non-commutative rings was the Scottish mathematician Wedderburn.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Ring_theory.html (1890 words)

	Free radical addition - Wikipedia, the free encyclopedia
		In one specific type of radical addition called self-terminating oxidative radical cyclization, alkynes are oxidized to ketones with intramolecular ring closure and the radical species are inorganic rather than carbon based.
		As an example a nitrate radical is generated by photolysis of CAN which reacts with an alkyne to generate first a very reactive vinyl radical and then via a 1,5-hydrogen atom transfer (HAT) and 5-exo-trig ring-closure a ketyl radical.
		The ketyl dislodges a nitrite radical which is not reactive enough for propagation and the ketone is formed.
	en.wikipedia.org /wiki/Radical_addition (373 words)

	PlanetMath: radical theory
		Radical theory is the study of radical properties and their interrelations.
		Cross-references: Jacobson radical, quasi-regularity, nilpotency is not a radical property, nil, nil is a radical property, nilpotent rings, isomorphic, simple rings, partition, contains, homomorphic, closed under, class, identity elements, ideal, ring, property, represent
		This is version 7 of radical theory, born on 2002-12-07, modified 2004-02-28.
	planetmath.org /encyclopedia/RadicalTheory.html (251 words)

	Radical Ions (Site not responding. Last check: 2007-08-30)
		This project began as a detailed study of the mechanism and kinetics of decay of several cyclopropyl-containing radical anions expected to undergo unimolecular rearrangement in analogy to the cyclopropylcarbinyl --> homoallyl neutral free radical rearrangement.
		Specifically, the kinetics associated with the ring opening of radical anions derived from cyclopropyl ketones were examined.
		For both types of processes, relief of cyclopropyl ring strain is not the sole mitigating factor associated with the rates of these rearrangements.
	www.chem.vt.edu /chem-dept/tanko/radion.htm (361 words)

	MILES IGERT (Site not responding. Last check: 2007-08-30)
		If electron transfer occurs, the radical cations generated from these compounds are expected to undergo ring opening (Scheme 1, path a), in direct analogy to the cyclopropylcarbinyl homoallyl neutral free radical rearrangement, generating a carbon-centered radical which will disrupt the enzyme active site and lead to inactivation.
		In addition to unimolecular ring opening, it is also possible that cyclopropyl amminium radical cations may ring open by a bimolecular, nucleophile-assisted pathway (Scheme 1, path b), a process which has been well-characterized for analogous ring openings of cyclopropylarene radical cations.
		The objective of this research is to characterize the mechanism and kinetics of ring opening of cyclopropyl amminium radical cations of direct relevance to enzymatic oxidations by electrochemical methods and nanosecond laser flash photolysis.
	www.chem.vt.edu /milesigert/Grimm.htm (246 words)

	Advances
		The diphenylcyclopropyl group is a “reporter” that will give a diphenylalkyl radical that can be detected by UV as in the reaction in Scheme 1.
		Synthetic sequence for a radical precursor for use in studies of the radical rearrangement catalyzed by methylmalonyl-CoA mutase.
		Cyclization gives a distonic radical cation that ring opens to the distonic diphenylalkyl radical cation that can be observed readily by its UV absorbance at 335 nm.
	www.chem.uic.edu /newcomb/advances.htm (301 words)

	A ring walk of methylene groups in toluene radical cations. An extension of the toluene-cycloheptatriene rearrangement ...
		An extension of the toluene-cycloheptatriene rearrangement of aromatic radical cations.
		Further, the 7-methoxy- norcaradiene radical ion is unstable and corresponds to a transition state between isomeric distonic intermediates differing by a 1,2-shift of the side chain.
		In contrast, the 7- methoxy-norcaradiene radical ion is the only intermediate of the DFT-MERP, and the distonic ion is the transition state for a 1,2-shift of the cyclopropane ring.
	www.impub.co.uk /abs/EMS09_0327.html (472 words)

	PlanetMath: Jacobson radical
		Note that the Jacobson radical can also be defined for rings without identity.
		This is version 15 of Jacobson radical, born on 2002-04-20, modified 2004-10-05.
		(Associative rings and algebras :: Radicals and radical properties of rings :: Jacobson radical, quasimultiplication)
	planetmath.org /encyclopedia/JacobsonRadical.html (106 words)

	Wikinfo \| Radical (Site not responding. Last check: 2007-08-30)
		Radical is derived from the Latin word radix, which means "pertaining to the root(s)".
		the n-th radical or root of a number a, written as √[n]a, which is a number whose n-th power is a (see radical (mathematics)).
		the Jacobson radical of a ring, which is an important ideal.
	www.wikinfo.org /wiki.php?title=Radical (248 words)

	Von Neumann Ring
		The subring of a von neumann ring is von neumann.
		If s is the quotient of a von neumann ring r, pull y ∈ s back to y′ in r, find x′ in r, and map this forward to x in s, making s von neumann.
		Thus the ring of endomorphisms is von neumann, where the selection of g is not unique.
	www.mathreference.com /ring-jr,vonring.html (741 words)

	Session J12 - Mini-Symposium: Cavity Ring-Down Spectroscopy.
		The ultraviolet absorption spectrum of the propargyl radical (H2C-C\equivCH) was re-examined in the wavelength regions of 235-260 nm and 320-360 nm, using the very sensitive, high resolution cavity ring-down spectroscopic (CRDS) technique.
		The radical was formed by excimer laser photolysis of propargyl chloride and allene, which were observed to produce identical spectra and kinetic behavior.
		The generation and decay of these radicals in the presence of excess amounts of a molecular reactant inside a high-quality optical cavity were monitored by the decay times of injected photons from a pulsed tunable dye laser.
	flux.aps.org /meetings/YR97/BAPSAPR97/abs/S1140.html (1005 words)

	Goethe-Institut London - Der Ring des Nibelungen
		Out went 'ensembles' (people singing together at the same time) so the audience could hear the words better; out went solo 'arias' (one person singing alone about how they feel) so the story moved along faster; and there were almost no 'choruses' (large numbers of people singing together) because its not true to life.
		To put The Ring onstage, you had to have more 'special effects' than any one theatre show had needed before - fire, water, very fast changes from one space to another, people suddenly vanishing etc. Remember this was more than 125 years ago, before the use of electricity or modern machinery in theatres.
		Like a novel, The Ring works on many different levels at the same time: as a sword and sorcery epic, as a warning about the dangers of the industrial revolution, as a discussion about whether man is more important than God.
	www.goethe.de /ins/gb/lon/pro/ring/teachersnotes/ks3/opera.htm (548 words)

	PH: RE: Radical SR8 to smash 'Ring record?
		With the launch of its SR8 track monster, Radical has made it its mission to circulate round the Nurburgring in under seven minutes, according to today's Autocar.
		Radical director Mick Hyde said that he'd studied the video of the SR3's lap and while he said it was a great lap, "it wasn’t perfect".
		The whole point of testing a car at the 'ring is that it is a very good test of a car's all-round ability, as it has some very bumpy bits, a couple of top speed bits and a few smooth bits.
	www.petrolheads.co.uk /gassing/topic.asp?f=83&t=151429 (981 words)

	Anesthetic polyorganophosphazenes - Patent 4495174
		A long-acting, local anesthetic, comprising a polymeric phosphazene backbone, and 2-amino-4-picoline radical having local anesthetic activity and an amino functional group on the ring of said radical through which said radical is covalently attached to the phosphazene backbone by a phosphorous-nitrogen single bond is disclosed along with medicaments containing such anesthetics.
		The local anesthetic of claim 1, wherein said organic radical is a radical of butethamine.
		a polymeric phosphazene backbone, and an organic radical having local anesthetic activity which is an ester of p-aminobenzoic acid and an amino functional group on a phenyl ring through which said radical is covalently attached to said phosphazene backbone by a phosphorous-nitrogen single bond.
	www.freepatentsonline.com /4495174.html (6233 words)

	IPC 6 English version C07H !A-C07H 23/00
		"saccharide radical" which is derived from acyclic polyhydroxy-aldehydes or acyclic polyhydroxy-ketones, or from their cyclic tautomers, by removing hydrogen atoms or by replacing hetero bonds to oxygen by the same number of hetero bonds to halogen, nitrogen, sulfur, selenium, or tellurium, in accordance with either of the following definitions:
		In this group, acyl radicals directly attached to hetero atoms of the saccharide radicals are not considered as substituted hydrocarbon radicals.
		attached to non-adjacent ring carbon atoms of the cyclohexane rings, e.g.
	www.wipo.int /classifications/fulltext/new_ipc/ipc6/ec07h.htm (1116 words)

	Video: Radical Round the 'Ring - Jalopnik
		The Radical SR8 could be one of the most economical ways to go really freaking fast and actually make a corner without testing Euclid's solution (tangents can hurt).
		The Radical SR8, which is street legal, holds the outright lap record for the 'Ring among production cars.
		The outright lap record overall was set in 1983 by the late Stefan Bellof, teammate of Jacky Ickx, in a Porsche 956 at 6:11.13.
	www.jalopnik.com /cars/novelties/video-radical-round-the-ring-162022.php (447 words)

	MTH-3E30 : Ring Theory
		In the course the basic results of non-commutative ring theory will be proved and the following topics are included: simple and semi-simple rings, division rings, radicals and the elementary theory of modules.
		Overview: Ring theory has many applications in mathematics and thanks to the re-discovery of its connections to physics in the last fifteen years is playing an ever more important role.
		One of the most powerful and efficient methods in non-commutative ring theory is the analysis of their representations.
	www.mth.uea.ac.uk /maths/syllabuses/9900/3E3001.html (335 words)

	Sapphire Ring Jewels - Swiss Jewel Company
		Ring Jewels serve as radical or sleeve bearings used with a straight cylindrical shaft.
		Rugged straight hole rings restrict lateral movement to a minimum but require accurate alignment when the clearance between pivot and bearing is closely held.
		Where thrust load is continuous, an endstone is usually combined with the ring jewel.
	www.swissjewel.com /sapphire_ring_jewels.htm (130 words)

	Stabilizing the Trp 191 radical (Site not responding. Last check: 2007-08-30)
		The structure of CcP is designed to focus a substantial negative electrostatic potential upon the indole ring of Trp 191.
		When the indole ring is removed by a Trp 191 -> Gly mutation, not only does indole refuse to occupy this cavity, but a potassium ion (yellow sphere) occupies the cavity instead.
		Additional structural features that contribute to local negative electrostatic potential include: dipole interactions from the carbonyl oxygen atoms of residues 175 and 177 (white), the negative dipole at the C- terminus of the helix that terminates at His 175 (not shown), and the carboxylate of heme pyrrole IV.
	chem-faculty.ucsd.edu /kraut/radical.html (309 words)

	Spectroscopic and Kinetic Investigations of the Propargyl Radical Using (Site not responding. Last check: 2007-08-30)
		The ultraviolet absorption spectrum of the propargyl radical (H
		The radical was formed by excimer laser photolysis of propargyl chloride, propargyl bromide, methyl acetylene, and allene, all of which were observed to produce identical spectra.
		No evidence of the predicted higher energy transitions was observed in the wavelength ranges 220 nm - 230 nm, 238 nm - 252 nm, or 264 nm - 282 nm, however a strong absorption due to chlorine atom addition products in the propargyl chloride system was observed near 240 nm.
	www.nist.gov /crds/propargyl.htm (174 words)

	.beta.-.gamma.-Unsaturated ketones and isoprenoid 2,6 diones, a process for producing the same and their use as ...
		R.sub.3 is an allylic radical with 3-5 carbon atoms, or an aromatic radical ring which, if desired, may be a benzyl radical carrying at most two further substituents, the substituents being up to two alkyl or alkoxyalkyl radicals with 1-3 carbon atoms and/or up to two halogen atoms; and
		R.sub.4 and R.sub.5 represent hydrogen, or alkyl or alkoxyalkyl radicals with 1-6 carbon atoms, alkenyl radicals with 2-6 carbon atoms, or phenyl groups having, if desired, up to two further substituents, the substituents being optionally up to two alkyl or alkoxyalkyl groups with 1-3 carbon atoms and/or or two halogen atoms.
		A further modification of the invention relates to compounds which are derived from formulas I and II by addition of hydrogen to at least one olefinic or carbonyl double bond.
	www.freepatentsonline.com /4385185.html (2876 words)

	ANTI- Press - The Promise Ring
		As one of the most prominent practitioners of the subgenre called emo, the Promise Ring has accrued a fan base that has grown comfortable with guitarist Davey von Bohlen's astringent pop songs.
		To a man, the Promise Ring had grown weary of carrying the emo mantle for its fans and of trying to please its constituency before its own needs were met.
		The Promise Ring decamped to Farnham, a rural hamlet outside London, to live and record in a country house with Stephen Street, a producer whose credits include albums with the Smiths and Blur.
	www.anti.com /press.php?id=19&pid=432 (1051 words)

	U.S. Patent: 5162588 - Aromatic compounds, a process for preparation thereof and use of same as perfuming ingredients - ...
		It is generally accepted that, in musky aromatic compounds whose benzene ring possesses an acyl group substituent, sterical hindrance of this functional group can lead to loss of odor [see, for example, M. Beets, Structure-Activity Relationships in Human Chemoreception, 207, ASP Ltd. London (1978)].
		Thus, any attempt to further substitute the benzene ring in the following basic structural skeleton for the aromatic compounds of interest ##STR17## would have been discouraged from the start.
		The synthesis represented in Scheme IV makes it possible to prepare symmetrical hydrocarbons wherein the two methyl groups substituting the benzene ring are equivalent, said hydrocarbons being easily oxidized with Ce (IV) to yield a mixture of aldehydes of formula (II) which can be separated by gas chromatography.
	www.everypatent.com /comp/pat5162588.html (8803 words)

	The Curran Research Group - Projects
		In the gymnomitrene synthesis, we developed a novel tandem radical cyclization which yields the tricyclo[5.3.1.0]undecane ring system in a single synthetic transformation from an acyclic precursor.
		All of the syntheses require the synthesis of the bicyclo[3.3.0] octane portion followed by sequential annulation of the 6-membered ring.
		The radical cyclization was performed using tris(trimethylsilyl)silane, as more traditional tin reagents were found to give large amounts of monocylized reduction products.
	radical.chem.pitt.edu /projects/tandem.html (324 words)

	Websites For Socialism
		This webring is dedicated to the purpose of socialism and other forms of radical thought.
		Radical Politics Online is a site dedicated to the cause of socialism and other radical forms of thought.
		We remain to be part of a school of thought committed to the replacement of corporate regimes by the institution of economic democracy on an international scale.
	u.webring.com /hub?ring=websitesforsocia (680 words)

	Cornell Chemistry Faculty Research - (Site not responding. Last check: 2007-08-30)
		In living free-radical polymerization, we are investigating novel functionalized nitroxyl radicals that operate at lower temperatures and can tolerate a broad scope of monomers.
		Synthesis of macromonomers and comb polymers using consecutive controlled free radical and cationic ring-opening polymerizations.
		One-pot, one-step, block copolymerization by simultaneous free radical and either cationic ring-opening or anionic ring-opening polymerizations.
	www.chem.cornell.edu /faculty/index.asp?fac=43 (569 words)

	Current Organic Chemistry, Volume 6, No. 11, 2002
		Exo-substituted cyclobutanones are employed to construct cis-fused seven- and eight-membered rings, spiro-annulated medium rings, large rings, and cyclopropanecontaining compounds.
		The cyclization of dichlorocyclobutanones followed by TMSI-induced ring opening is another ring expansion strategy for the construction of some novel ring systems.
		Cyclobutanones used for free radical reactions are readily prepared by well-established [2 + 2] cycloadditions of ketenes with various olefins.
	www.bentham.org /coc/contabs/coc6-11.htm (571 words)

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