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Topic: Ring ideal

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Prime ideal

Principal ideal

Ring (mathematics)

Commutative ring

Principal ideal domain

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	Ideal (ring theory) - Wikipedia, the free encyclopedia
		In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
		The even integers form an ideal in the ring Z of all integers; it is usually denoted by 2Z.
		The sum and the intersection of ideals is again an ideal; with these two operations as join and meet, the set of all ideals of a given ring forms a lattice.
	en.wikipedia.org /wiki/Ring_ideal (1343 words)

	Ring ideal: Definition and Links by Encyclopedian.com - All about Ring ideal (Site not responding. Last check: 2007-11-05)
		Conversely, if we start with a two-sided ideal I of R, then we may define a congruence relation ~ on R as follows: a ~ b if and only if b - a is in I.
		The map p from R to R/I defined by p(a) = a + R is a surjective ring homomorphism (or regular epimorphism[?]) whose kernel is the original ideal I.
		For instance, in general rings one studies prime ideals instead of prime numbers, one defines coprime ideals as a generalization of coprime numbers, and one can prove a generalized Chinese remainder theorem about ideals.
	www.encyclopedian.com /ri/Ring-ideal.html (1314 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		abstract algebra, an ideal is a special subset of a ring which generalizes important properties of integers.
		A proper ideal I is called a prime ideal if for all ab in I it follows either a or b in I.
		The sum and the intersection of ideals is again an ideal; with these two operations as join and meet, the set of all ideals of a given ring forms a
	en-cyclopedia.com /wiki/Maximal_ideal (1185 words)

	boolean ring (Site not responding. Last check: 2007-11-05)
		A map between two Boolean rings is a ring homomorphism if and only if it is a homomorphism of the corresponding Boolean algebras.
		Furthermore, a subset of a Boolean ring is a ring ideal (prime ring ideal, maximal ring ideal) if and only if it is an order ideal (prime order ideal, maximal order ideal) of the Boolean algebra.
		The quotient ring of a Boolean ring modulo a ring ideal corresponds to the factor algebra of the corresponding Boolean algebra modulo the corresponding order ideal.
	www.yourencyclopedia.net /Boolean_ring (465 words)

	Boolean algebra - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-05)
		The zero element of this ring coincides with the 0 of the Boolean algebra; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
		This ring has the property that a * a = a for all a in A; rings with this property are called Boolean rings.
		This notion of ideal coincides with the notion of ring ideal in the Boolean ring A.
	encyclopedia.worldsearch.com /boolean_algebra.htm (1587 words)

	The Ideal Engagement Ring \| Tension Set Engagement Settings (Site not responding. Last check: 2007-11-05)
		Every tension set ring is closely inspected to ensure it meets the high standards.
		Tension set ring settings are manufactured with special alloys by a sophisticated technique which enables the metal to retain it's memory.
		Every ring is individually and meticulously crafted using the most advanced technologies, machinery and careful quality control.
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	Finite Rings (Site not responding. Last check: 2007-11-05)
		An element of a ring that does not lie in any maximal ideal is a unit (by applying Zorn’s lemma; however, this is not required for finite rings or finite dimensional algebras).
		Hence the intersection of all prime ideals is also the ideal consisting of all nilpotent elements of a ring; this ideal is called the nil radical of the ring.
		The Nilpotency of the Nil radical of a Noetherian Ring.
	www.imsc.ernet.in /~kapil/geometry/caag/finite.html (2519 words)

	Ideal Cut Diamond in Custom 18kt Ring - Bijoux Extraordinaire
		Six smaller ideal cut diamonds are channel set along the shoulders of this stately 18kt gold ring.
		Each component of the ring has to be meticulously crafted and then they must all be brought together as an artistic whole.
		The six smaller round diamonds set along the shoulders of the ring weigh a total of 0.9 carats and are also ideal cut, F color and VS clarity.
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	[No title]
		Based on the characterisaion in Theorem 3, we give an algorithm for constructing strong Gröbner bases over a principal ideal ring, generalising thus Buchberger's results to a this type of ring.
		We use the fact that a ring is a principal ideal ring if and only if it is isomorphic to a direct product of principal ideal domains and Artinian chain rings.
		Using Theorem 4 these results can be generalised to principal ideal rings and the restriction on the length of the code can be removed.
	www-calfor.lip6.fr /ICPSS/papers/40Sa/40Sa.htm (959 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-05)
		In fact, this translates directly into proper ideals of Z. Another point to be kept in mind is that the union of all proper ideals is generally not an ideal.
		We could also, instead of the union of ideals, consider the operation defined as = L, where L is the smallest ideal containing J and K.
		By definition, L is indeed an ideal, but, if J and K are proper ideals, it does not follow that L is a proper ideal.
	mathforum.org /library/drmath/view/65137.html (954 words)

	High quality Gold Ring Jewelry is guaranteed and we offer the lowest prices on the internet.
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		Gold Ring 6.0 - 6.5 mm The lengths are 16 inches, 18 inches and 20 inches.
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	[No title] (Site not responding. Last check: 2007-11-05)
		In mathematics, a Boolean ring R is a
		Furthermore, a subset of a Boolean ring is a
		ring ideal (prime ring ideal, maximal ring ideal) if and only if it is an
	en-cyclopedia.com /wiki/Boolean_ring (386 words)

	Token Ring/IEEE 802.5
		IBM Token Ring network stations are directly connected to MSAUs, which can be wired together to form one large ring (see Figure 9-2).
		Token Ring and IEEE 802.5 are two principal examples of token-passing networks (FDDI is the other).
		While the information frame is circling the ring, no token is on the network (unless the ring supports early token release), which means that other stations wanting to transmit must wait.
	www.cisco.com /univercd/cc/td/doc/cisintwk/ito_doc/tokenrng.htm (1624 words)

	Ring ideal : Ideal (ring)
		An ideal I is called proper if I isn't equal to R.
		All is still licensed under the GNU FDL.
		A little wooden bridge over; but the latter did not seem disposed to profit by this silent.
	www.termsdefined.net /id/ideal-(ring).html (1477 words)

	Ideals, Principal ideals, Principal ideal rings and Quotient rings.
		Ideals, Principal ideals, Principal ideal rings and Quotient rings.
		A subring of a ring such that * is commutative, i.e.
		This means that Z would be a principal ideal ring.
	hemsidor.torget.se /users/m/mauritz/math/alg/ideal.htm (279 words)

	Ideal Ring Constitution
		The purpose of this organization shall be to encourage comradery and community service and to serve as a forum for information of interest to math students.
		The Ideal Ring will not discriminate on the basis of age, color, gender, handicapper status, height, marital status, national origin, political persuasion, race, religion, sexual orientation, veteran status, or weight.
		An officer who fails to remain a member in good standing or that fails to do his or her duty as written in the constitution may be removed from office.
	www.msu.edu /~ideal/constitution.htm (387 words)

	Ideal Cut Diamond Engagement Ring - Bijoux Extraordinaire
		The diamonds in this ring are ideal cut with a GIA color grade of D and an IF (internally flawless) clarity grade.
		Many mass produced, cast rings with low cost settings have the gemstones all set on the same plane which gives the ring a boxy, flat-top appearance.
		We often make three-stone rings with an 18kt yellow gold band and platinum double-rung setting, but they can also be made in all yellow gold, all white gold or all platinum.
	www.jewelryexpert.com /catalog/cd4.htm (716 words)

	Theory Ideal (Isabelle2005: October 2005)
		is_ideal I; a ∈ I; b ∈ I ] ==> a + b ∈ I
		is_ideal I; a ∈ I ] ==> a * r ∈ I
		(ideal_of {a} ⊂ ideal_of {b}) = (b dvd a ∧ ¬ a dvd b)
	isabelle.in.tum.de /library/HOL/HOL-Algebra/Ideal.html (348 words)

	Errata for the book: Computations in algebraic geometry with Macaulay 2 (Site not responding. Last check: 2007-11-05)
		The routine ignores any relations between the variables in the ring "S" of "I", so it will fail unless the ring is a polynomial ring.
		(2) It uses "t" as a global variable, so fails if the ideal "I" is in a ring already using "t" as an indeterminate.
		(3) It also uses the first "r" letters of the alphabet as global variables, where "r" is the number of generators of the ideal "I", so fails if the ideal is in a ring using any of those letters as variables.
	www.math.uiuc.edu /Macaulay2/Book/errata.html (234 words)

	[No title]
		This is the default -- since it appears to be on the average the fastest."), -- (TT "Strategy => TorusDeformation", "--Iterates the intersection -- between the ideal and a random torus deformation of it.
		This -- avoids computing GBs and the improvement can be very dramatic -- for very dense ideals."), -- (TT "Strategy => TorusDeformation2", "--Iterates the intersection -- between the ideal and two random torus deformation of it.
		The matrix m is the given -- linear -- presentation map, and R is the target ring.
	www.math.sunysb.edu /~sorin/m2/orlik-solomon.m2 (191 words)

	(quote /,Ring,Ideal) (Site not responding. Last check: 2007-11-05)
		, unless R has a name, or one of the rings R is a quotient ring of has a name.
		Quotient rings are bulky objects, because they contain a Groebner basis for their ideals, so only quotients of
		will be a brand new ring, and its elements will be incompatible with the elements of previously created quotient rings for the same ideal.
	www.mi.uni-koeln.de /b/Macaulay2/html/108.html (78 words)

	Aerobie Sprint Flying Ring (Site not responding. Last check: 2007-11-05)
		And that goes for the Sprint Ring - a smaller, lighter version of the original Aerobie Flying Ring.
		Ideal for those that enjoy the incredible Guinness World Distance Record setting performance of Aerobie rings but have a smaller area in which to play.
		The Sprint Flying Ring measures 10 inches in diameter.
	www.recommendedshopping.com /aerobie_sprint_flying_ring.html (84 words)

	Singular 2-0-6 Manual: show
		id may be a ring or a qring.
		In this case the minimal polynomial is displayed, and, for a qring, also the defining ideal.
		id may be of type list but the list must not contain a ring.
	www.singular.uni-kl.de /Manual/html/sing_424.htm (91 words)

	Rings internet sources (Site not responding. Last check: 2007-11-05)
		Detailed research all over the net resulted in this site about Rings and loose emerald cut diamond and pick out just a couple of the very best sites for you to visit.
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	rings.informationadvice.info (615 words)

	Diamond Ring - Ideal Cut Diamond Engagement Ring (Site not responding. Last check: 2007-11-05)
		A diamond should look bright.....like football or egg, then there's the ideal cut diamond, a form of round diamond.....and subsequent...
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	diamond-ring-depot.com /idealcutdiamondengagementring.html (571 words)

	Build Your Own Engagement Ring: The Ultimate Tutorial
		It's a flawless, ideally cut, perfectly clear and colorless one carat diamond in a platinum double tapered sapphire baguette setting.
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	www.organizedregistry.com /engagement_ring/build_your_own.php (1348 words)

	Ring -- the class of all rings (Site not responding. Last check: 2007-11-05)
		The type Ring is a member of the class Type.
		Each object of class Ring is called a ring.
		Each ring is also a member of class Type.
	www.math.uiuc.edu /Macaulay2/Manual/0037.html (374 words)

	Strong Gröbner bases for polynomials over a principal ideal ring (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Abstract: Gröbner bases have been generalised to polynomials over a commutative ring A in several ways.
		Several authors have shown that strong Gröbner bases can be effectively constructed over a principal ideal domain.
		We show that this extends to any principal ideal ring: we characterise Gröbner bases and strong Gröbner bases when A is a principal ideal ring.
	citeseer.ist.psu.edu /norton01strong.html (351 words)

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	www.engagement-ring-shopper.com /engagement-ring-tradition (722 words)

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