# ring

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## 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 lawcommutative law,
in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7.
; associative lawassociative law,
in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9.
; distributive lawdistributive law.
In mathematics, given any two operations, symbolized by * and +, the first operation, *, is distributive over the second, +, if a*(b+c)=(a*b)+(a*c) for all possible choices of a, b, and c.
). A commutative ring is one in which the commutative law also holds for multiplication. Examples of commutative rings are the sets of integers (see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
) and real numbers. Square matrices (see matrixmatrix,
in mathematics, a rectangular array of elements (e.g., numbers) considered as a single entity. A matrix is distinguished by the number of rows and columns it contains. The matrix

is a 2×3 (read "2 by 3") matrix, because it contains 2 rows and 3 columns.
) furnish examples of non-communtative rings.

## ring,

in astronomy, relatively thin band of rocks and dust and ice particles that orbit around a planet in the planet's equatorial plane. All four of the giant planets in the solar system—JupiterJupiter
, in astronomy, 5th planet from the sun and largest planet of the solar system. Astronomical and Physical Characteristics

Jupiter's orbit lies beyond the asteroid belt at a mean distance of 483.6 million mi (778.
, SaturnSaturn,
in astronomy, 6th planet from the sun. Astronomical and Physical Characteristics of Saturn

Saturn's orbit lies between those of Jupiter and Uranus; its mean distance from the sun is c.886 million mi (1.
, UranusUranus
, in astronomy, 7th planet from the sun, at a mean distance of 1.78 billion mi (2.87 billion km), with an orbit lying between those of Saturn and Neptune; its period of revolution is slightly more than 84 years.
, and NeptuneNeptune,
in astronomy, 8th planet from the sun at a mean distance of about 2.8 billion mi (4.5 billion km) with an orbit lying between those of Uranus and the dwarf planet Pluto; its period of revolution is about 165 years.
— have rings, although only those of Saturn are easily visible. The origin of the rings is unknown. One theory is that they may have been formed from moons that were shattered by the impact of comets and meteoroids. Another holds that they might be the remnants of moons or comets that came within the planet's Roche limitRoche limit,
the closest distance that a celestial body held together only by its own gravity can come to a planet without being pulled apart by the planet's tidal (gravitational) force. This distance depends on the densities of the two bodies and the orbit of the celestial body.
and were broken up by gravitational forces. In the case of the E ring, it is now known that geyserlike eruptions on Enceladus are a source of the material in the ring.

Saturn has seven rings designated alphabetically as A through G in the order of their discovery. Two additional rings, designated as R/2004 S1 and R/2004 S2 were discovered in images returned to earth from the Cassini space probe in 2004. In 2009 the Spitzer Space Telescope discovered an enormous but faint dust ring that originates in material removed from the moon Phoebe by impacts. From the planet outward, the rings are D, C, B, A, R/2004 S1, R/2004 S2, F, G, E, and the Phoebe ring. With named gaps occupying the space between several of the rings, Saturn's rings are a highly complex structure stretching almost 167,770 mi (270,000 km) from the planet's center to the farthest edge of ring E; the Phoebe ring extends from 3.7 to 7.4 million mi (6 to 12 million km). The rings are not perfectly circular, and the gaps are not completely empty. The Columbo and Maxwell Gaps separate the C and B rings, the Cassini Division and Huygens Gap separate the B and A rings, and the Encke Division and Keeler Gap separate the A and R/2004 S1 rings. Except for the A and B rings, which are separated primarily by the 2,920-mi-wide (4,700-km) Cassini Division, and the Phoebe ring, the rings are relatively close to one another. Most of the rings appear to be composed of small pieces of water ice mixed with a small amount of rocky material in a wide range of particle sizes, from 1 in. (2.5 cm) to 33 ft (10 m)—although there may be an occasional object as large as a mile (1.6 km) in diameter. The Phoebe ring is composed of dust particles about 10 microns in size. Data returned by Cassini indicates that the rings are not uniform; for example, the B ring is very different from the A and C rings (which are similar to one another) found on either side of it. The Phoebe ring is tilted at a 27° angle from the plane of the other rings and, unlike the other rings, orbits Saturn with a retrograde motion. Several of Saturn's small moons appear to be shepherd satellites, maintaining the shape of the rings through gravitational interactions, and there are also ring arcs associated with several moons.

Jupiter's rings are similar to those of Saturn but much smaller and fainter. The main ring is about 4,300 mi (7,000 km) wide and has an abrupt outer boundary 80,000 mi (128,940 km) from the center of the planet. The inner main ring is formed from dust and ice particles kicked up when meteoroids collide with the small Jovian satellites Metus and Adrastea. The particles then spiral slowly in toward Jupiter. At its inner edge the main ring merges into the halo. A broad, faint band of dust and particles, the halo is about 6,200 mi (10,000 km) thick and stretches halfway from the main ring down to the top of Jupiter's atmosphere. A pair of broad, faint gossamer rings are located just outside the main ring, one bounded by the orbit of the Jovian shepherd satellite Amalthea and the other by the orbit Thebe.

Uranus has a thin elliptical band of eleven faint, narrow rings composed of ice, rock, and dust. Stretching outward from the planet, the rings are named 1986 U2R, Six, Five, Four, Alpha, Beta, Eta, Gamma, Delta, 1986 U1R, and Epsilon; the distance from the planetary center to the Epsilon ring is 31,750 mi (51,140 km). The rings are distinctly different from those of Jupiter and Saturn. A tenuous distribution of fine dust is scattered throughout the ring system, and the rings all are the same flat, dark color (perhaps from methane or black-carbon ice coating the rock), unlike Saturn's bright rings. The nine main rings consist of a single layer of particles, the monolayer, which had not previously been seen in planetary rings; the particles are kept from drifting away by several shepherd satellites. Because there are ringlets and incomplete rings and a varying opacity in several rings, it is believed that the Uranian ring system may be the remnants of a small moon.

Neptune has four almost circular faint rings composed of small rocks and dust. The rings are not uniform in density and thickness; the thicker parts of the rings are called ring arcs. Stretching outward from the planet, the rings are named Galle, Le Verrier (whose outer extension is called Lassel), Arago, and Adams (which includes the ring arcs Liberty, Equality, and Fraternity); the distance from the planetary center to the Adams ring is 39,000 mi (62,930 km). The forces responsible for the development of ring arcs and ring extensions are not well understood, but shepherd satellites and gravitational forces attributable to Neptune's moons are thought to play a significant role. Earth-based observations indicate that the rings are less stable than was originally believed.

## ring,

small ornamental hoop usually worn on finger or thumb, but it may be attached to the ear or the nose. Finger rings made of bronze, gold, and silver from the period c.2500–1500 B.C. have been found in the Indus valley in India; in Egypt rings from c.1600 B.C. served as a symbol of status and were exchanged as a pledge or seal of faith. They were often also used as money. The signet ring grew from the custom of wearing a cylindrical seal suspended from the arm or neck, developed in Egypt, and was widely adopted as a seal of authority. Numerous rings were worn by Egyptian women, sometimes as many as three on a finger. In Greece gold bands were worn; later they were engraved with cameos or intaglios. Talismanic rings, endowed with many charms and powers, were also worn. In the middle and latter part of the Roman civilization the type of ring worn was governed by law. Iron rings were worn by the mass of the people; gold rings were reserved for those of civil or military rank. Later the gold ring was permitted to freeborn citizens, silver to freedmen, and iron to slaves. The Romans also used poison rings for assassination or suicide in the case of capture by an enemy. In addition there were key rings, which, worn by a matron, symbolized her authority to carry the keys of the house. The betrothal ring, used by Egyptians, Greeks, and Romans, was adopted by early Christians in the 2d cent. and later evolved into the wedding ring. The engagement ring set with a precious gem came into use in the Middle Ages; the diamond attained popularity in the 15th cent. and became customary c.1800. From the Middle Ages rings have figured in the coronation of kings and the consecration of bishops as emblems of authority or mystical significance. Since that time a gold seal ring (Fisherman's ring) with an intaglio of St. Peter in a fishing boat has been given each pope and is destroyed when he dies. By the 16th cent. the extravagant use of rings had reached its height. Highly decorated with enamel and jewels, they were sometimes worn on every finger and on several joints. At that time, too, the gold wedding band became popular, and signet rings were engraved with the family crest. Later, memorial rings and mourning rings became fashionable.

### Bibliography

See W. Jones, Finger-Ring Lore (1898, repr. 1968); S. Bury, Rings (1985).

or

## ring

(bar -nardz) see Orion.

## Ring

an ornament worn on the finger among most of the world’s peoples. Bone rings originated during the Paleolithic, and metal rings during the Bronze Age.

Seal rings with carved inscriptions or designs were common in ancient Egypt. The wax impression made with the ring served as the owner’s signature. Later, the Aegean peoples, the Greeks, and the Etruscans wore seal rings, which were often set with gems. In the Roman Republic senators and equites wore gold finger rings; ordinary citizens wore iron ones. Under the Roman Empire this rule was abolished, and in the third century all freeborn persons were granted the right to wear gold rings, and all freedmen the right to wear silver rings. In ancient Rus’ gold and silver rings with engraved or embossed designs were favored in the cities. Copper rings with geometric designs were worn in the countryside. In succeeding periods, gold or silver rings set with precious or semiprecious stones became common.

The ring worn by a Catholic bishop is a symbol of authority. Among many of the peoples of the world smooth, unornamented rings are used as wedding bands, following a custom that originated in ancient Rome.

A. V. ARTSIKHOVSKII

## Ring

a simple form of monopolistic association. It is a temporary speculative combination of several capitalists for the purpose of buying up a commodity on the market or holding the commodity in storage until it can be most profitably sold at inflated prices. The first rings appeared in the Middle Ages and were agreements between individual merchants for the establishment of monopolies. Under the conditions of industrial capitalism, rings usually appeared in times of general shortages of commodities resulting from, for example, wars or natural disasters. In the epoch of imperialism rings have been used by the monopolies as one means of establishing monopoly prices in order to increase profit.

## What does it mean when you dream about a ring?

To dream of a ring as a piece of jewelry may indicate the expression of commitment to a relationship or to marriage. A ring can also represent the completion and wholeness that the dreamer is experiencing within themselves. In the case of a ringing sound, it may indicate that the dreamer needs to shift his or her attention to some issue or situation in their waking life. (See also Jewels/Jewelry, Necklace).

## ring

[riŋ]
(computer science)
A cyclic arrangement of data elements, usually including a specified entry pointer.
(design engineering)
A tie member or chain link; tension or compression applied through the center of the ring produces bending moment, shear, and normal force on radial sections.
(mathematics)
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.
(organic chemistry)
A closed loop of bonded atoms in a chemical structure, for example, benzene or cyclohexane.

## Ring

A tie member or chain link. Tension or compression applied through the center of a ring produces bending moment, shear, and normal force on radial sections. Because shear stress is zero at the boundaries of the section where bending stress is maximum, it is usually neglected.

## ring

worn on fourth finger, left hand, symbolizes love. [Western Folklore: Brewer Dictionary, 919]
See: Love

## ring

represents the cyclical nature of time. [Pop. Culture: Cirlot, 273–274]
See: Time

## ring

1
1. a square apron or raised platform, marked off by ropes, in which contestants box or wrestle
2. the ring the sport of boxing
3. an area reserved for betting at a racecourse
4. a circular strip of bark cut from a tree or branch, esp in order to kill it
5. Geometry the area of space lying between two concentric circles
6. Maths a set that is subject to two binary operations, addition and multiplication, such that the set is an Abelian group under addition and is closed under multiplication, this latter operation being associative
7. Botany short for annual ring
8. Chem a closed loop of atoms in a molecule
9. Astronomy any of the thin circular bands of small bodies orbiting a giant planet, esp Saturn

## ring

2
Electronics the damped oscillatory wave produced by a circuit that rings

## ring

(1) The ringer line in an early telephone cable. See tip and ring.

(2) A privilege level in the computer. When software is assigned to a ring, it may be limited to executing certain instructions in the computer. Ring 0 has the highest privilege and can access all instructions. The operating system or the virtual memory monitor (VMM) resides in ring 0.

Applications typically reside in ring 3, which has a lower priority, and are prohibited from executing instructions that address the hardware. If an application attempts to execute a prohibited instruction, an error indication (fault) is generated. Rings 1 and 2 are available in some computers, but may or may not be used. See virtual machine monitor.

## Ring

(dreams)
Are you dreaming about ornamental jewelry or merely noise? If you are dreaming the former, the ring may be symbolic of your commitments and promises. The ring can been seen from a larger point of view as a circle, which is a symbol of completion and wholeness. If the ring is a noise, it can be interpreted as an attention-seeking message. Consider those things that you have been ignoring or unwilling to look at and examine the details of your dream. Some people believe that a type of pleasant ringing may be a “joyful” noise and that it is the sound of God. In that case this dream is a real blessing!
References in periodicals archive ?
You can tell who is holding the ring," Qahtan said later, "because he sweats and shakes and makes more sudden movements than the others.
The trouble with buying a diamond ring online has always boiled down to one simple detail: it is difficult to make such a huge decision without actually holding the ring in your hand.
Somewhere between the two - and uneasily holding the ring between them -- is U.

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