
	Where results make sense

Topic: Spectrum of a ring

Related Topics

Category of commutative rings

Topology glossary

Topological space

Zariski topology

Compact space

Greenstone

In the News (Thu 16 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Spectrum of a ring - Wikipedia, the free encyclopedia
		In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by Spec(R), is defined to be the set of all proper prime ideals of R.
		The spectrum of R therefore consists of the points of A together with elements for all subvarieties of A.
		By studying spectra of polynomial rings instead of algebraic sets with Zariski topology, one can generalize the concepts of algebraic geometry to non-algebraically closed fields and beyond, eventually arriving at the language of schemes.
	en.wikipedia.org /wiki/Spectrum_of_a_ring (1001 words)

	Spectrum (Site not responding. Last check: 2007-10-19)
		The power spectrum is the distribution of the energy of a function in the frequency domain, which is actually the same as the magnitude of the frequency spectrum.
		The spectrum of a matrix is the spectrum of an operator where the matrix is considered as operator.
		The meanings of spectrum in some other disciplines, including pharmacology, politics, and psychology evolved by analogy with the meanings in the physical sciences: just as dispersed colored light ranged from one end of the rainbow to the other, so also other things that range from one extreme to another were called spectra.
	www.casimiro.com /wiki/en/wikipedia/s/sp/spectrum.html (619 words)

	Localization of a ring - Wikipedia, the free encyclopedia
		Given a ring R and a subset S, one wants to construct some ring R* and ring homomorphism from R to R, such that the image of S consists of units (invertible elements) in R.
		The term localization originates in algebraic geometry: if R is a ring of functions defined on some geometric object (algebraic variety) V, and one wants to study this variety "locally" near a point p, then one considers the set S of all functions which are non-zero at p and localizes R with respect to S.
		In the theory of the spectrum of a ring, these localizations are used to identify basic open sets in Spec(R).
	en.wikipedia.org /wiki/Localization_of_a_ring (871 words)

	NationMaster - Encyclopedia: Spectrum of a ring (Site not responding. Last check: 2007-10-19)
		In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law.
		In mathematics, a locally ringed space (or local ringed space) is, intuitively speaking, a space together with, for each of its open sets, a commutative ring the elements of which are thought of as functions defined on that open set.
		In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring which generalizes important properties of integers.
	www.nationmaster.com /encyclopedia/Spectrum-of-a-ring (1936 words)

	Spectrum of a ring - the free encyclopedia (Site not responding. Last check: 2007-10-19)
		In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by Spec(R), is defined to be the set of all prime ideals of R.
		Every ring homomorphism f : R → S induces a continuous map Spec(f) : Spec(S) → Spec(R) (since the preimage of any primeideal in S is a prime ideal in R).
		The spectrum of R therefore consists of the points of A together with elements for all subvarieties of A.The points of A are closed in the spectrum, while the elements corresponding to subvarieties have a closure consisting ofall their points and subvarieties.
	www.the-free-web-encyclopedia.com /default.asp?t=Spectrum_of_a_ring (909 words)

	Spectrum of a ring: Definition and Links by Encyclopedian.com
		In abstract algebra and algebraic geometry, the spectrum of a commutative ring R is defined to be the set of all prime ideals of R.
		Note that every ring homomorphism f : R → S induces a continuous map Spec(f) : Spec(S) → Spec(R) (since the preimage of any prime ideal in S is a prime ideal in R).
		By studying spectra of polynomial rings instead of algebraic sets with Zariski topology, one can generalize the concepts of algebraic geometry to non-algebraically closed fields and eventually to schemes.
	www.encyclopedian.com /sp/Spectrum-of-a-ring.html (701 words)

	Spectrum
		Spectrum is an Australian state funded service providing consultation, training, treatment and research in relation to people with severe and borderline personality disorder who are at risk from serious self harm.
		Spectrum serves clients who typically have a diagnosis of borderline personality disorder, severe interpersonal difficulties and a long history of self-harm and/or suicide attempts.
		The Spectrum approach to treatment is based on an acknowledgement of the importance of early experience, including, in many cases, the effects of trauma and deprivation.
	www.spectrum-bpd.com /front.htm (721 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-19)
		A ringed space that is locally isomorphic to an affine scheme.
		are in bijective correspondence with the ring homomorphisms
		In the construction of a concrete scheme one most frequently uses the concepts of an affine or projective spectrum (see Affine morphism; Projective scheme), including the definition of a subscheme by a sheaf of ideals.
	eom.springer.de /s/s083340.htm (1114 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-19)
		The structure space of a biregular ring (see Regular ring (in the sense of von Neumann)) is locally compact and totally disconnected.
		It is used to represent a biregular ring in the form of a ring of continuous functions with compact supports.
		This is an extension of the notion of the spectrum space of maximal ideals of a commutative ring (cf.
	eom.springer.de /S/s090690.htm (156 words)

	Spectra of Rings
		The spectrum of a ring is always compact, thus cannot be isomorphic to Euclidean n-space.
		Thus in fact every proper ideal of the ring R of continuous functions on a compact interval has a common zero, hence the ideal is contained in the maximal ideal corresponding to that point, and by maximality must equal it.
		Indeed the definition of dimension of a spectrum is (one less than) the length of a strictly nested chain of prime ideals, such as (0), (x), (x,y), in K[x,y], where K is a field.
	www.physicsforums.com /showthread.php?t=32806 (1881 words)

	[No title]
		Suppose R is a ring spectrum and v is a finitary vn-element.
		Suppose R is a ring spectrum and v is a vn-element.
		Indeed, it is the Thom spectrum of the composite * !
	www.math.purdue.edu /research/atopology/Hovey/vnelements.txt (9076 words)

	About Spectrum Geophysics
		Spectrum Geophysics will continue to develop and expand the worldwide market for near-surface geophysics by providing innovative, superior, and cost-effective field services, complete client satisfaction, and a great working environment for our staff.
		Spectrum utilizes both the Geonics EM-61, a high sensitivity metal detector, and the Geonics EM-31, a terrain conductivity meter.
		Spectrum holds frequent staff meetings, not only to collectively find better ways to serve our clients, but also to constantly reinforce our vision of providing superior geophysical services and complete client satisfaction.
	www.spectrum-geophysics.com /companyinfo.html (794 words)

	PlanetMath: algebraic geometry
		Of course, if the ring is the complex numbers, we can apply the highly succesful theories of complex analysis and complex manifolds to address the problems; many powerful tools are available; de Rham cohomology, singular homology, Hodge theory, spectral sequences and many others.
		In particular, a scheme is a topological space with an associated sheaf, the structure sheaf, which defines which functions of sheaves are considered morphisms in the category of schemes.
		If the extra structure also includes an embedding of the ring of integers of a totally real number field into the endomorphism ring of the abelian variety, one obtains the Hilbert moduli space.
	planetmath.org /encyclopedia/AlgebraicGeometry.html (2516 words)

	National Synchrotron Light Source
		The THz region of the electromagnetic spectrum lies between the infrared and the microwave.
		Source research efforts in past years predict that the achievable stable CSR power and spectrum of a ring-based source are strongly dependent on ring RF frequency and gap voltage.
		Beam longitudinal instabilities were observed in both the radiation spectrum and time domain signals as well as in the beam longitudinal profile measurements.
	www.nsls.bnl.gov /newsroom/science/2006/06-Wang.htm (872 words)

	Spectrum of a ring (Site not responding. Last check: 2007-10-19)
		In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by Spec(R), is defined to be the set ofall prime ideals of R.
		It is commonly augmented with a topology, the Zariski topology, and with a structure sheaf, turning itinto a locally ringed space.
		Every ring homomorphism f : R → S induces a continuous map Spec(f) : Spec(S) → Spec(R) (since the preimage ofany prime ideal in S is a prime ideal in R).
	www.therfcc.org /spectrum-of-a-ring-215094.html (603 words)

	Colorful Spectrum Diamond treated Titanium rings (Site not responding. Last check: 2007-10-19)
		Spectrum Diamond film colors are extremely durable and respond well to most daily wear situations.
		With Spectrum Diamond treatment, the actual coating is tougher than the titanium it covers, allowing you to enjoy the brilliant coloration on the entire outer surface of the ring.
		The option of having your ring treated with Spectrum Diamond is provided in the "Finish" area on the order page for all rings that are compatible with this process.
	www.titaniumrings.com /spectrumdiamond.html (469 words)

	PlanetMath: scheme
		These families can even span different characteristics, which can be a powerful tool for applying the tools of characteristic zero geometry to problems in positive characteristic.
		For many problems, the points of the underlying topological space of a scheme do not represent what we want to work with.
		An affine variety corresponds to the prime spectrum of its coordinate ring, and a projective variety has an open cover by affine pieces each of which is an affine variety, and hence an affine scheme.
	planetmath.org /encyclopedia/Scheme.html (641 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		This is because the only sphere that can be a ring spectrum is S and it can only be a ring spectrum in one way.
		If E is an R-module spectrum for some ring spectrum R, then the unit map pi_* S --> pi_* R is a split monomorphism of rings.
		In particular, if E is a ring spectrum, then E=S. (because then the retraction pi_* E --> pi_* F(E,E) is a monomorphism).
	www.lehigh.edu /~dmd1/mh78 (256 words)

	IEEE Spectrum: Ring of Steel II (Site not responding. Last check: 2007-10-19)
		IEEE Spectrum: Ring of Steel II Font Size: A A A
		The so-called ring of steel, inaugurated in 1998, is a network of cameras that provides comprehensive video coverage of a large part of the City.
		The idea for a ring of steel was born in the early 1990s after a bombing campaign by Northern Irish terrorists left four people dead, dozens injured, and parts of the City of London in ruins.
	www.spectrum.ieee.org /jul06/4106 (1134 words)

	American Gem Trade Association - 2002 Spectrum Awards Winners (Site not responding. Last check: 2007-10-19)
		AGTA Spectrum Awards is an annual natural colored gemstone and cultured pearl jewelry design competition.
		Platinum and 18K yellow gold ring with 1.66 ct tanzanite, 1.39 ct rubellite tourmaline and (8) princess cut yellow sapphires.76 tcw.
		Ring "Parallels." Square antique cushion tsavorite garnet 1.20 ct and (24) diamonds.71 tcw.
	www.agta.org /consumer/spectrum/2002winners.htm (755 words)

	Varieties and Schemes for Dummies, Part I \| The String Coffee Table
		As the table indicates, algebraic geometry is motivated by the desire to understand the geometry of the spectrum of rings of polynomials.
		Essentially, a regular function on the spectrum of a ring will, as for varieties, be a function on the spectrum which is locally given by the quotient of two elements of the ring.
		In fact, these sheaves have the special property (as I vaguely indicated above) that the stalk over each point is a local ring (and hence something that we may interpret as a ring of coordinate functions regarded at a given point).
	golem.ph.utexas.edu /string/archives/000849.html (2701 words)

	Waveshaping
		equals one, this just amounts to ring modulating the sinusoid by a sinusoid of the same frequency, whose result we described in the previous section: the output is a DC (zero-frequency) sinusoid plus a sinusoid at twice the original frequency.
		In contrast with ring modulation, which is a linear function of its input signal, waveshaping is nonlinear.
		DJ85], and from there you can go on to build any desired static spectrum (Example E05.chebychev.pd demonstrates this.) Generating families of spectra by waveshaping a sinusoid of variable amplitude turns out to be trickier, although several interesting special cases have been found, some of which are developed in detail in Chapter 6.
	www-crca.ucsd.edu /~msp/techniques/latest/book-html/node77.html (1229 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		We show that the associated stable homotopy theory is completely determined by a ring spectrum functorially associated with the algebraic theory.
		For the theory of commutative algebras we obtain a ring spectrum which is related to Andre-Quillen homology via certain spectral sequences.
		We show that the (co-)homology of an algebraic theory is isomorphic to the topological Hochschild (co-)homology of the parameterizing ring spectrum.
	hopf.math.purdue.edu /Schwede/stable.abstract (114 words)

	On the K-theory spectrum of a ring of algebraic integers, by W. G. Dwyer and S. A. Mitchell (Site not responding. Last check: 2007-10-19)
		On the K-theory spectrum of a ring of algebraic integers, by W. Dwyer and S. Mitchell
		An explicit recipe for using classical invariants of R to construct a candidate C for the algebraic K-theory spectrum of R. If the Lichtenbaum/Quillen conjecture is true, then C essentially is the algebraic K-theory spectrum.
		The spectrum C is constructed from the arithmetic of R in a way which extends Quillen's construction of FPsi(q) from the Galois theory of a finite field F(q).
	www.math.uiuc.edu /K-theory/0037 (136 words)

	Spectrum Coatings - Astronomical Telescope Mirrors
		Spectrum Coatings --- A State of the Art Optical Coating Company.
		Producing Front Surface Mirror coatings, Anti-Reflection, Beamsplitter, hot and cold mirrors, dichroic filters that meet and exceed the standards of the optical thin film industry.
		Unlike the majority of thin film companies, at Spectrum Coatings we utilize our technology to accommodate a wide variety of uses for the unique properties of optical coatings.
	www.spectrum-coatings.com (132 words)

	Spectrum of a ring
		It is commonly augmented with a topology, the Zariski topology, and with a structure sheaf, turning it into a locally ringed space.
		Every ring homomorphism f : R → S induces a continuous map Spec(f) : Spec(S) → Spec(R) (since the preimage of any prime ideal in S is a prime ideal in R).
		Wapipedia > Index > S > Sp > Spectrum of a ring
	www.wapipedia.com /wikipedia/mobiletopic.aspx?cur_title=Affine_scheme (727 words)

	SPECTRUM OF A RING (Site not responding. Last check: 2007-10-19)
		In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by Spec, is defined to be the set of all prime ideals of R.
		Spec can be turned into a topological space as follows: a subset V of Spec is closed if and only if there exists a subset I of R such that V consists of all those prime ideals in R that contain I.
		It is licensed under the GNU free documentation license.
	www.yotor.org /wiki/en/sp/Spectrum%20of%20a%20ring.htm (642 words)

Try your search on: Qwika (all wikis)