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Topic: Ring (mathematics)

Related Topics

Ring theory

Commutative ring

Field (mathematics)

Subring

Local ring

Formal power series

Trivial ring

Ideal (ring theory)

Prime ideal

Principal ideal

Class number

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	Chapter 9: Mathematics
		Known as a Kaleidocycle, or Flexahedron, the toy was invented years ago by a bored mathematics student.
		Now pinch that end closed, so the tabs are glued to the paper, holding the snake's tail firmly in his mouth, forming a ring.
		When the glue is dry, you can now start turning the ring inside-out, pushing the center up from the bottom, and the outside parts down.
	sci-toys.com /scitoys/scitoys/mathematics/paper_ring.html (500 words)

	math lessons - Ring (mathematics)
		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.
		The split-complex plane D is a ring useful in modern physics and is a subring of the tessarines.
		Given a ring R and an ideal I of R, the quotient ring (or factor ring) R/I is the set of cosets of I together with the operations
	www.mathdaily.com /lessons/Ring_(mathematics) (1084 words)

	Ring (mathematics) (Site not responding. Last check: )
		In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have similar (but not identical) properties to those familiar from the integers.
		Rings that also satisfy commutativity for multiplication (such as the ring of integers) are called commutative rings.
		The center of a ring R is the set of elements of R that commute with every element of R; that is, c lies in the center if cr=rc for every r in R.
	www.guideofpills.com /Ring_(mathematics).html (1247 words)

	Springer Online Reference Works
		A ring on which a an action ( "multiplication" ) of elements of the ring by elements from a fixed set
		The most commonly studied rings with operators are those with an associative-commutative ring of operators possessing a unit element.
		This type of ring is usually called an algebra over a commutative ring, and also a linear algebra.
	eom.springer.de /R/r082450.htm (358 words)

	Ring (mathematics) - Wikipedia, the free encyclopedia
		A ring is a generalization of the integers, which itself is an example of a ring.
		Rings that also satisfy commutativity for multiplication (such as the ring of integers) are called commutative rings.
		Given a ring R and an ideal I of R, the quotient ring (or factor ring) R/I is the set of cosets of I together with the operations
	en.wikipedia.org /wiki/Ring_(mathematics) (1365 words)

	Wikipedia: Ring
		The Opera cycle The Ring of the Nibelung is often referred to as "the Ring"
		The Ring is a horror motion picture that is a remake of a Japanese cult movie, Ring.
		Ring is also the title of a science fiction novel by Stephen Baxter
	www.factbook.org /wikipedia/en/r/ri/ring.html (142 words)

	ring - Wiktionary
		The mathematics sense was introduced by mathematician David Hilbert in 1892, a contraction of the German Zahlring.
		(mathematics) An algebraic structure which is a group under addition and a monoid under multiplication.
		It was equal to half a quarter, i.e., is identical with the coomb of the eastern counties.
	en.wiktionary.org /wiki/ring (469 words)

	AllRefer.com - ring, mathematical system (Mathematics) - Encyclopedia
		ring, in mathematics, system consisting of a set R of elements and two binary operations, such that addition makes R a commutative group and multiplication is associative and distributes over addition (see commutative law; associative law; distributive law).
		A commutative ring is one in which the commutative law also holds for multiplication.
		Examples of commutative rings are the sets of integers (see number) and real numbers.
	reference.allrefer.com /encyclopedia/R/ring2.html (186 words)

	Algebraic Areas of Mathematics
		We have included here the combinatorial topics and number theory; each is arguably a distinctive area of mathematics but (as the MathMap suggests) these parts of mathematics, shown in shades of red, share definite affinities.
		The use of algebra is pervasive in mathematics.
		Of particular interest are several classes of rings of interest in number theory, field theory, algebraic geometry, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra.
	www.math.niu.edu /~rusin/known-math/index/tour_alg.html (1113 words)

	Product (mathematics) - Wikipédia
		The dot product and cross product are forms of multiplication of vectors.
		Products in rings and fields of many kinds.
		It is often possible to form the product of two (or more) mathematical objects to form another object of the same kind, e.g.
	su.wikipedia.org /wiki/Mathematical_product (150 words)

	HJM, Vol. 29, No. 3, 2003
		If R is a unital ring, then the left multiplications by elements of R obviously form endomorphisms of the additive group of R. In fact they form a group direct summand of the endomorphism ring and if the complement is trivial, then these rings are called E-rings which are well-studied.
		Finally, we show that in ZFC there exists an almost-free ring R of minimal uncountable cardinality such that the endomorphism ring of R is isomorphic to the direct sum of the integers and R itself.
		An hereditarily decomposable circle-like continuum, not homeomorphic to the circle, that admits arbitrarily small periodic homeomorphisms semiconjugate to arbitrarily small rigid rotations at the level of the tranche decomposition to the circle is constructed.
	www.math.uh.edu /~hjm/Vol29-3.html (2232 words)

	[No title]
		An algebraic system with two operations called multiplication and addition; the system is a commutative group relative to addition, and multiplication is associative, and is distributive with respect to addition.
		A ring of sets is a collection of sets where the union and difference of any two members is also a member.
		] A faint ring of Saturn inside ring B having an outer diameter of 114,000 miles (183,000 kilometers) and an inner diameter of 91,000 miles (146,000 kilometers).
	www.accessscience.com /Dictionary/R/R25/DictR25.html (2788 words)

	MANIFOLD-10: Mathematics of the 70s
		For the purposes of this note, rings are associative with unit element, and 'Noetherian' means that the maximum condition holds for left and right ideals.
		For a simple Noetherian ring, the requirement is just that every left and right ideal should be a projective module; this condition is satisfied by all simple rings with minimum condition, and by some without it.
		The endornorphism ring of P is a simple Noetherian ring, which has zero-divisors in general.
	www.jaworski.co.uk /m10/10_70s.html (1663 words)

	Mathematics
		The mathematics Web Ring enlists documents published in the World Wide Web of computers about the subjects of History of mathematics, Algebra, Arithmetics, Metrology, Spacemetry (Geometry), Topology, Trigonometry, or any other related topics, including Research and teaching of these disciplines.
		Mathematics is a science based on reasoning and deduction under strict logical principles, more than based on experience and induction.
		It is a collection of numeric examples, in the realm of finite, power modulus and curvacious mathematics.
	q.webring.com /hub?ring=mathematics&id=1&hub (362 words)

	The Noetherian Ring
		This past summer, the 25th anniversary of the American Women in Mathematics (AWM) culminated in the Julia Robinson Celebration of Women in Mathematics, a three-day conference in early July held at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California.
		Noetherian Ring members who attend the colloquium dinner afterwards benefit from the opportunity of engaging in dialogue with the speaker and interacting with the other faculty present.
		Thus, the Noetherian Ring has decided to begin raising funds for a university endowment, the interest of which would be used to support our Speaker Series in the years to come.
	math.berkeley.edu /publications/newsletter/1996/noetherianarticle.html (600 words)

	The Noetherian Ring at Berkeley
		AWM Workshop during the Joint Mathematics Meetings in San Francisco, women at MIT were motivated to form the MIT Noetherian Ring.
		Noetherian Ring at the University of Wisconsin (Madison),
		Women in Mathematics at the University of Maryland College Park, and Women in Mathematics at the University of Pennsylvania.
	math.berkeley.edu /~nring (535 words)

	HJM, Vol. 30, No. 2, 2004
		Also, we say that R is a phi-Bezout ring if phi(I) is a principal ideal of phi(R) for every finitely generated nonnil ideal I of R. We show that the theories of phi-Prüfer and phi-Bezout rings resemble that of Prüfer and Bezout domains.
		In a manner analogous to the commutative case, the zero-divisor graph of a noncommutative ring R can be defined as the directed graph G. It has been shown that G is not a tournament if R is a finite ring with no nontrivial nilpotent elements and the graph has more than one vertex.
		This article also shows that G cannot be a network for a finite ring R. These results are used to determine which directed graphs on 1, 2, or 3 vertices can be realized as G. Finally, it is shown that for a finite ring R, G has an even number of directed edges.
	www.math.uh.edu /~hjm/Vol30-2.html (1741 words)

	MTH-2A24 : Algebra II
		Apart from the general notions of rings, ideals and homomorphisms, the course deals with the theory of polynomials, an introduction to field theory and the theory of factorization.
		The notions of principal ideal and divisibility are steps to higher arithmetics with divisibility theory, and to the theory of polynomial rings.
		Homomorphism and isomorphism, quotient ring, quotient ring of a maximal ideal, finite fields.
	www.mth.uea.ac.uk /maths/syllabuses/9900/2A2400.html (521 words)

	11: Number theory
		Number theory is one of the oldest branches of pure mathematics, and one of the largest.
		The correct construction for the investigation of this phenomenon is usually a local ring such as the p-adic integers.
		The algebraic structure of the ring of integers is similar to that of other commutative rings such as rings of polynomials.
	www.math.niu.edu /~rusin/known-math/index/11-XX.html (2572 words)

	Puzzle Worksheet: Stringing the Ring
		One such trick is to get a ring dropped around the outside of a loop of string to become tied to that loop with a knot.
		While holding one end of the loop, grab the ring and slowly pull it in the opposite direction.
		If you hold the correct end and grab the ring in exactly the right place, you should be able to knot the ring to the string.
	www.aimsedu.org /puzzle/stringring/srings2.html (209 words)

	Clyde Davenport's Commutative Hypercomplex Math Page (Site not responding. Last check: )
		What he didn't realize was that the quaternions form a group ring [i.e., the 1,i,j,k elements and their negatives form a group of order eight (the quaternion group, of course), and elements of the form 1x+iy+jz+kw, with x,y,z,w real, form a ring].
		The fact that we exclusively use the quaternion case (vector analysis) in science and engineering apparently stems from the fact that it was discovered first and the others were not examined for potential application when they were eventually uncovered.
		All of the other conditions for a ring are satisfied, as well; see [Davenport(3), 1991] for details.
	home.usit.net /~cmdaven/hyprcplx.htm (4408 words)

	[No title] (Site not responding. Last check: )
		] A commutative ring with a unit element in which every ideal is a principal ideal.
		In classical physics and in special relativity, the principle that the laws of physics take the same mathematical form in all inertial reference frames.
		In general relativity, the principle that the laws of physics take the same mathematical form in all conceivable curvilinear coordinate systems.
	www.accessscience.com /Dictionary/P/P43/DictP43.html (2683 words)

	Ring Ideals
		Construction of rings and left-, right-, and bi-modules over a ring.
		The correctness of the generic algorithms of Brown and Henrici concerning addition and multiplication in fraction fields.
		The ring of integers, euclidean rings and modulo integers.
	mizar.uwb.edu.pl /JFM/Vol12/ideal_1.html (185 words)

	Mathematics Factorial: Rumors "Ring" True
		If you count the existence of a ring on my left hand as a making it official, than yes, it is official.
		I was perturbed Monday thru Wednesday of finals week (well, when I had a spare moment to think about something other than school) because Josh had not yet asked "the question." I had figured that he'd surely propose before Christmas break.
		He was even mean and taunted me Wednesday night about the dangers of hiding ring in champagne.
	www.shadowcouncil.org /mathteach/archives/003968.html (794 words)

	[No title]
		Java is highly object oriented but not very common in mathematical context.
		Object oriented programming should be a main feature in CAS (as user defined functions a couple of years ago).
		Mathematical software should use object oriented terminology instead of "reinventing the wheel".
	ring.perisic.com /info/OOPMath1/OOPMath1.PPT (492 words)

	The Noetherian Ring at UW-Madison (Site not responding. Last check: )
		The Noetherian Ring at UW-Madison is a gathering of women graduate students, faculty, postdocs, and academic staff members in the Mathematics Department.
		The Ring was founded in 1996 by Cheryl Grood, at that time a graduate student here.
		She modeled the gathering after the Noetherian Ring at UC-Berkeley.
	www.math.wisc.edu /~hollings/noethring (140 words)

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