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Topic: Radical of an ideal

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Nilradical

Glossary of ring theory

Lie group

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	ScienceDaily: Radical of an ideal (Site not responding. Last check: 2007-10-12)
		In ring theory, a branch of mathematics, the radical of an ideal is a kind of completion of the ideal.
		The radical of an ideal I in a commutative ring R, denoted by Rad(I) or âI, is defined as
		Hence, the nilradical of R/P is {0}, and its preimage, being P, is a radical ideal.
	www.sciencedaily.com /encyclopedia/radical_of_an_ideal (1598 words)

	Radical - Wikipedia, the free encyclopedia
		the radical of an algebraic group is a concept in algebraic group theory.
		the radical of an ideal is an important concept in abstract algebra.
		in linguistics, a radical consonant involves the root of the tongue.
	en.wikipedia.org /wiki/Radical (295 words)

	Encyclopedia: Radical (Site not responding. Last check: 2007-10-12)
		In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety.
		Radical consonants are articulated with the root (base) of the tongue in the throat.
		Radical Republicans were a group of politicians during the Reconstruction era that believed freed slaves should have political and social equality with all other citizens.
	www.nationmaster.com /encyclopedia/Radical (929 words)

	Jacobson radical (Site not responding. Last check: 2007-10-12)
		In 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.
	www.bopedia.com /en/wikipedia/j/ja/jacobson_radical.html (460 words)

	Radical Philosophy - Articles - Autumn 1994
		An ideal is made answerable to reason when, under some description, it is shown to merit allegiance.
		Postmodern critics, however, attack the ideal of authenticity not as a symptom of cultural decline, but on the grounds that it is a con or a subterfuge for domination.
		Characteristically, however, the postmodernist critic of the ideal of authenticity extends this line of thought to the conclusion that the idea of an authentic self is a delusion enmeshed within the sinister purposes of mastery and exclusion.
	www.radicalphilosophy.com /default.asp?channel_id=2188&editorial_id=11040 (962 words)

	radical of an ideal (Site not responding. Last check: 2007-10-12)
		In ring theory, a branch of mathematics, the radical of a ring isolates certain bad properties of the ring.
		There are several different kinds of radicals, such as the nilradical and the Jacobson radical, as well as a theory of general radical properties.
		If P is a prime ideal, then R/P is an integral domain, so it cannot have zero divisors, and in particular it cannot have nilpotents.
	www.yourencyclopedia.net /radical_of_an_ideal.html (662 words)

	Radical of an ideal - Wikipedia, the free encyclopedia
		The nilradical is the most common radical in commutative algebra, and there it is usually called just the radical.
		The Jacobson radical of R is the intersection of the annihilators of all simple right R-modules.
		If the ring R is a finitely generated Z-algebra, then the nilradical is equal to the Jacobson radical, and more generally: the radical of any ideal I will always be equal to the intersection of all the maximal ideals of R that contain I.
	www.encyclopedia-online.info /Nilradical (634 words)

	PlanetMath: radical of an ideal
		"radical of an ideal" is owned by saforres.
		See Also: prime radical, radical of an integer, Jacobson radical, Hilbert's Nullstellensatz, algebraic sets and polynomial ideals
		This is version 10 of radical of an ideal, born on 2002-04-19, modified 2003-02-20.
	www.planetmath.org /encyclopedia/RadicalIdeal.html (82 words)

	Radical of an ideal (Site not responding. Last check: 2007-10-12)
		There are severaldifferent kinds of radicals, such as the nilradical and the Jacobson radical, as well as a theory of generalradical properties.
		It is written Rad(R) or√R. It is useful to define the nilradical of an ideal I in R.
		An ideal that is equal to its radical is called aradical ideal and is said to be radical.
	www.therfcc.org /radical-of-an-ideal-210828.html (576 words)

	PlanetMath: proof of characterizations of the Jacobson radical
		Observe that 5) follows after the equivalence of 1) - 4) is established, since 4) is independent of the choice of left or right ideals.
		So the intersection of all left primitive ideals will be contained in the intersection of all maximal left ideals.
		This is version 27 of proof of characterizations of the Jacobson radical, born on 2002-06-26, modified 2005-03-15.
	www.planetmath.org /encyclopedia/ProofOfCharacterizationsOfTheJacobsonRadical.html (247 words)

	S/R 5: Radical Democracy: A Contested/ing Terrain (Sandilands)
		First, radical democracy is, clearly and crucially, government by the root, by "the people." Although there are a number of different ways of thinking about "the people," I would argue that radical democracy understands "the people" to be constituted through diverse experiences, needs, and desires as both individuals and members of communities.
		Thus, radical democracy is a form of politics that recognizes diversity, and invites participation from a variety of social spaces.
		In a radical democracy, it is precisely the double-movement between proliferation of specificities and constitution of a "we" that defines its difference from other versions of democracy: neither the universal nor the particular is sacred.
	www.greens.org /s-r/05/05-13.html (1521 words)

	Gene therapy may be a cure for post-radical prostatectomy erectile dysfunction
		Neuropathic ED results from damage to the nerves essential to achieving and maintaining an erection and is experienced by 79.6 percent of men who undergo radical prostatectomies.
		In the study, researchers injected herpes simplex virus vectors that deliver neurotrophic factors, factors that facilitate the recovery of injured nerves, into the corpus cavernosum or cavernous nerve of rats at the time of cryo-injury to the cavernous nerve.
		Radical prostatectomy is used to treat the early stages of prostate cancer by surgically removing the prostate gland and surrounding tissue.
	www.eurekalert.org /pub_releases/2003-04/uopm-gtm042203.php (374 words)

	Mediated Radical Polymerization
		All of these processes involve the presence of a capping agent (nitroxyl radical, halogen atom, organometal moiety, or other molecular fragment) to react reversibly with the propagating radical to generate a non-radical species which is unreactive.
		In this bound state the propagating radical is stable or dormant and unable to participate in termination or chain transfer processes.
		The term mediated radical polymerization (MRP) is not only descriptive of a wide range of radical polymerizations carried out in the presence of agents to modify the reactivity of the propagating species but avoids the confusion associated with the terms living free radical, living radical, controlled radical polymerization and the like.
	www.polyacs.org /nomcl/pmse.medrad.html (771 words)

	Broadening Care, Discerning Worth: The Environmental Contributions of Minimalist Religious Naturalis
		An implication of minimalism is the notion that the divine may best be conceived of as a collection of natural forces or ideals.
		This continuing challenge of ideals is the ideal aspect of the transcendent.
		We turn also to the power of a religious naturalism that emphasizes both the continuing transcendence of challenging ideals and the relative transcendence of surpassing resources to give us the challenge and the empowerment to undergo the drastic paradigm shifts which may be needed as we face our exponentially worsening ecological crisis.
	www.religion-online.org /showarticle.asp?title=2846 (4885 words)

	ABSTRACT ALGEBRA ON LINE: Ideal Theory of Commutative Rings
		An integral domain D is called a Dedekind domain if each proper ideal of D can be written as a product of a finite number of prime ideals of D. We will show in Theorem 12.2.4 that a Dedekind domain has some of the properties of a principal ideal domain.
		Let D be an integral domain with quotient field F, and let I be an ideal of D that is invertible when considered as a fractional ideal.
		I is the intersection of all prime ideals of R that contain I. In any principal ideal domain, our next definitions both reduce to the statement that the ideal in question is generated by a power of an irreducible element.
	www.math.niu.edu /~beachy/aaol/commutative.html (2296 words)

	Radical Retropubic Prostatectomy (Site not responding. Last check: 2007-10-12)
		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, which is a number whose n -th power is a (see radical(mathematics)).
		In some cases, the doctor ca 152: In radical* retropubic prostatectomy, the doctor removes the entire prostate and nearb 153: In radical* perineal prostatectomy, the doctor removes the entire prostate through a 156: the doctor removes the lymph nodes before doing a prostatectomy.
	www.elusiveeye.com /side38183-radical-retropubic-prostatectomy.html (417 words)

	Radical Philosophy - print friendly
		They have reacted to the realization that we cannot ever tell with certainty whether our ideal of community is not an instrument for the oppression of some people by asserting that fully inclusive communities are impossible.
		Young's choice of metaphors in conveying this objection to the ideal of community is particularly illuminating.
		Such an ideal of the transparency of subjects to one another denies the difference...
	www.radicalphilosophy.com /print.asp?editorial_id=9862 (761 words)

	Jacobson Radical
		The jacobson radical of a ring r, written jac(r), is the intersection of all the maximal left ideals of r.
		Given an element y in r, several conditions are equivalent to y lying in jac(r).
		If h is a right ideal, then 1-yx is right invertable for every x, y is in the intersection of maximal right ideals, y is in jac(r), and h is in jac(r).
	www.mathreference.com /ring-jr,intro.html (806 words)

	The Doctrine of Inalienable Rights (Site not responding. Last check: 2007-10-12)
		I am not an environmentalist, in the sense that I oppose the building of this or the construction of that simply because it would require the destruction of forest or the relocation of wildlife.
		Saudi Arabia is an enemy country because it is the home of, and financier of the Wahhibi brand of Islam that is the backbone of militant Islamo-fascists.
		Thus an act or omission which, of itself or by intention, causes death in order to eliminate suffering constitutes a murder gravely contrary to the dignity of the human person and to the respect due to the living God, his Creator.
	members.aol.com /paprtigr (19875 words)

	Jacobson radical (Site not responding. Last check: 2007-10-12)
		The Jacobson radical of the ring Z /8 Z (see modular arithmetic) is 2 Z /8 Z.
		Unless R is the trivial ring {0} the radical is always a proper ideal in R.
		The Jacobson radical of the ring R /J(R) is zero.
	www.freeglossary.com /Jacobson_radical (626 words)

	CAMPBELTOWN - LoveToKnow Article on CAMPBELTOWN (Site not responding. Last check: 2007-10-12)
		Near the village of Southen.d is Machrireoch, the duke of Argylls shooting-lodge, an old structure modernized, commanding superb views of the Firth of Clyde and its islands, and of Ireland.
		On the rock of Dunaverty stood the castle of Macdonald of the Isles, who was dispossessed by the Campbells in the beginning of the 17th century.
		He had become its leader as a conciliator of the various sections, and it was as a conciliator, ready to sympathize with the strong views of all sections of his following, that he kept the party together, while his colleagues went their own ways in their own departments.
	www.1911ency.org /C/CA/CAMPBELTOWN.htm (946 words)

	Abstracts of Papers
		The paper presents a unified description of stable ideals of a continuous nest agebra as the kernels of limits of certain diagonal compressions.
		In an earlier paper (The Invertibles are Connected in Infinite Multiplicity Nest Algebras) it was shown that the group of inveribles in a nest algebra is connected, provided the algebra has infinite multiplicity.
		An example is presented of a maximal triangular subalgebra of B(H) which is not norm-closed.
	www.math.unl.edu /~jorr/research/abstracts.html (765 words)

	Publications of the SPACES team
		The field extension which is generated by the radicals which appear in the result is always minimal, when only one root is produced, as well as when all roots are given.
		In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z. Li.
		An algorithm is given and proved which reduces the computations of these zeros to the resolution of a single univariate equation whose degree is the number of common zeros.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	Radical of an ideal - Definition up Erdmond.Com
		Let ''a'' and ''b'' be nilpotent elements of ''R'' with ''an'' = 0 and ''bm'' = 0.
		The nilradical is the most common radical in commutative_algebra, and there it is usually called just the ''radical''.
		If ''P'' is a prime_ideal, then ''R/P'' is an integral_domain, so it cannot have zero_divisors, and in particular it cannot have nilpotents.
	www.erdmond.com /Radical_of_an_ideal.html (602 words)

	THE BELGRAVIA DISPATCH: The Myth of a Radical Bush Foreign Policy
		Radical seems to be one of Krugman's favorite words.
		Bush, of course, a radical in the Krugmanian universe.
		Radical is typically defined as "(f)avoring or effecting fundamental or revolutionary changes in current practices, conditions, or institutions".
	www.belgraviadispatch.com /archives/001205.html (857 words)

	Jacobson radical - The Jiggies Reference Guide (Site not responding. Last check: 2007-10-12)
		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 is named for Nathan Jacobson, who first studied the Jacobson radical.
		Rings with zero Jacobson radical are called semiprimitive rings.
	www.jiggies.com /reference/Jacobson_radical (489 words)

	Whither Judaism and The West ?
		What follows is the Conclusion of the last book("The Culture of Critique: An Evolutionary Analysis of Jewish Involvment in Twentieth-Century Intellectual and Political Movements") of the three-volume "Judaism as a Group Evolutionary Strategy" series, by Kevin MacDonald.
		One conclusion of this volume is that Jews have played a decisive role in developing highly influential intellectual and political movements that serve their interests in contemporary Western societies.
		There has been an enormous growth in Jewish power and influence in Western societies generally, particularly the United States.
	www.cosmotheism.net /articles/lastchap.html (749 words)

	A Little Radical Thinking
		While January is the beginning of the calendar year, it often seems natural to sit down at the end of summer to get a good fix on the year ahead.
		And for many entrepreneurs, an ideal goal is to have a steady, comfortable income, maximizing their flexibility and minimizing their stress.
		The goal is not to radically remake our business -- which, after all is growing nicely now -- but to keep our thinking fresh, to find ways to improve and enhance, not just innovate.
	www.inc.com /articles/2003/09/radical.html (778 words)

	ORAC Oxygen Radical Absorbance
		Free radicals are molecules with incomplete electron shells which make them more chemically reactive than those with complete electron shells.
		In humans, the most common form of free radicals is oxygen.
		When an oxygen molecule (O2) becomes electrically charged or "radicalized" it tries to steal electrons from other molecules, causing damage to the DNA and other molecules.
	www.prozactruth.com /orac.htm (297 words)

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