# Algebra vs. Ring — What's the Difference?

## Compare with Definitions

#### Algebra

Algebra (from Arabic: الجبر‎, romanized: al-jabr, lit. 'reunion of broken parts, bonesetting') is one of the broad areas of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.
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#### Ring

A small circular band, typically of precious metal and often set with one or more gemstones, worn on a finger as an ornament or a token of marriage, engagement, or authority
He had a silver ring on one finger
A bishop's ring
A diamond ring
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#### Algebra

A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
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#### Ring

A ring-shaped or circular object
An inflatable rubber ring
Fried onion rings
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#### Algebra

A set together with a pair of binary operations defined on the set. Usually, the set and the operations simultaneously form both a ring and a module.
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#### Ring

An enclosed space, surrounded by seating for spectators, in which a sport, performance, or show takes place
A circus ring
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#### Algebra

A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
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#### Ring

A group of people engaged in a shared enterprise, especially one involving illegal or unscrupulous activity
The police had been investigating the drug ring
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#### Algebra

The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
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#### Ring

A number of atoms bonded together to form a closed loop in a molecule
A benzene ring
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#### Algebra

The study of algebraic structures.
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#### Ring

A set of elements with two binary operations, addition and multiplication, the second being distributive over the first and associative.
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#### Algebra

A universal algebra.
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#### Ring

An act of ringing a bell, or the resonant sound caused by this
There was a ring at the door
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#### Algebra

An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
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#### Ring

A particular quality conveyed by something heard or expressed
The song had a curious ring of nostalgia to it
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#### Algebra

A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
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#### Ring

Surround (someone or something), especially for protection or containment
The courthouse was ringed with police
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#### Algebra

One of several other types of mathematical structure.
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#### Ring

Put an aluminium strip round the leg of (a bird) for subsequent identification
Only a small proportion of warblers are caught and ringed
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#### Algebra

(figurative) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.
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#### Ring

Fraudulently change the identity of (a motor vehicle), typically by changing its registration plate
There may be an organization which has ringed the stolen car to be resold
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#### Algebra

That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
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#### Ring

Short for ringbark
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#### Algebra

A treatise on this science.
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#### Ring

Make a clear resonant or vibrating sound
A shot rang out
A bell rang loudly
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#### Algebra

The mathematics of generalized arithmetical operations
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#### Ring

Call by telephone
Harriet rang Dorothy up next day
She rang to tell him the good news
I rang her this morning
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#### Ring

(of a place) resound or reverberate with (a sound or sounds)
The room rang with laughter
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#### Ring

A circular object, form, line, or arrangement.
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#### Ring

A small circular band, generally made of precious metal and often set with jewels, worn on the finger.
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#### Ring

A circular band used for carrying, holding, or containing something
A napkin ring.
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#### Ring

Rings(Sports) A pair of circular metal bands suspended in the air for gymnastic exercises, on which balancing and swinging maneuvers are performed while holding the bands as motionless as possible.
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#### Ring

A circular movement or course, as in dancing.
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#### Ring

An enclosed, usually circular area in which exhibitions, sports, or contests take place
A circus ring.
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#### Ring

A rectangular arena set off by stakes and ropes in which boxing or wrestling events are held.
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#### Ring

The sport of boxing.
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#### Ring

An enclosed area in which bets are placed at a racetrack.
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#### Ring

Bookmakers considered as a group.
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#### Ring

An exclusive group of people acting privately or illegally to advance their own interests
A drug ring.
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#### Ring

A political contest; a race.
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#### Ring

(Botany) An annual ring.
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#### Ring

(Mathematics) The area between two concentric circles; annulus.
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#### Ring

(Mathematics) A set of elements subject to the operations of addition and multiplication, in which the set is a commutative group under addition and associative under multiplication and in which the two operations are related by distributive laws.
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#### Ring

Any of the turns constituting a spiral or helix.
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#### Ring

(Chemistry) A group of atoms linked by bonds that may be represented graphically in polygonal form. Also called closed chain.
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#### Ring

The sound created by a bell or another sonorous vibrating object.
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#### Ring

A loud sound, especially one that is repeated or continued.
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#### Ring

A telephone call
Give me a ring when you have time.
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#### Ring

A suggestion of a particular quality
His offer has a suspicious ring.
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A set of bells.
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#### Ring

The act or an instance of sounding a bell.
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#### Ring

To surround with or as if with a ring; encircle
Guests ringed the coffee table.
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#### Ring

To form into a ring or rings.
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#### Ring

To ornament or supply with a ring or rings
Ringed the door knocker with a wreath of holly.
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#### Ring

To remove a circular strip of bark around the circumference of (a tree trunk or branch); girdle.
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#### Ring

To put a ring in the nose of (an animal).
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#### Ring

To hem in (animals) by riding in a circle around them.
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#### Ring

(Games) To toss a ring over (a peg), as in horseshoes.
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#### Ring

To form a ring or rings.
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#### Ring

To move, run, or fly in a spiral or circular course.
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#### Ring

To give forth a clear resonant sound.
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#### Ring

To cause something to ring.
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#### Ring

To sound a bell in order to summon someone
I'll ring for the maid.
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#### Ring

To have a sound or character suggestive of a particular quality
A story that rings true.
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#### Ring

To be filled with sound; resound
The room rang with the children's laughter.
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#### Ring

To hear a persistent humming or buzzing
My ears were ringing from the sound of the blast.
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#### Ring

To be filled with talk or rumor
The whole town rang with the bad news.
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#### Ring

To cause (a bell, for example) to ring.
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#### Ring

To produce (a sound) by or as if by ringing.
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#### Ring

To announce, proclaim, or signal by or as if by ringing
A clock that rings the hour.
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#### Ring

Chiefly British To call (someone) on the telephone. Often used with up
She rang me at noon. Let's ring her up and invite her.
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#### Ring

To test (a coin, for example) for quality by the sound it produces when struck against something.
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#### Ring

(physical) A solid object in the shape of a circle.
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#### Ring

A circumscribing object, (roughly) circular and hollow, looking like an annual ring, earring, finger ring etc.
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#### Ring

A round piece of (precious) metal worn around the finger or through the ear, nose, etc.
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#### Ring

(British) A bird band, a round piece of metal put around a bird's leg used for identification and studies of migration.
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#### Ring

(UK) A burner on a kitchen stove.
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#### Ring

In a jack plug, the connector between the tip and the sleeve.
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#### Ring

(historical) An instrument, formerly used for taking the sun's altitude, consisting of a brass ring suspended by a swivel, with a hole at one side through which a solar ray entering indicated the altitude on the graduated inner surface opposite.
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#### Ring

(botany) A flexible band partly or wholly encircling the spore cases of ferns.
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#### Ring

(physical) A group of objects arranged in a circle.
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#### Ring

A circular group of people or objects.
A ring of mushrooms growing in the wood
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#### Ring

(astronomy) A formation of various pieces of material orbiting around a planet or young star.
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#### Ring

(British) A large circular prehistoric stone construction such as Stonehenge.
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#### Ring

A piece of food in the shape of a ring.
Onion rings
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#### Ring

(internet) webring
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#### Ring

A place where some sports or exhibitions take place; notably a circular or comparable arena, such as a boxing ring or a circus ring; hence the field of a political contest.
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#### Ring

The open space in front of a racecourse stand, used for betting purposes.
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#### Ring

An exclusive group of people, usually involving some unethical or illegal practices. Category:en:Corruption
A crime ring; a prostitution ring; a bidding ring (at an auction sale)
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#### Ring

(chemistry) A group of atoms linked by bonds to form a closed chain in a molecule.
A benzene ring
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#### Ring

(geometry) A planar geometrical figure included between two concentric circles.
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#### Ring

(typography) A diacritical mark in the shape of a hollow circle placed above or under the letter; a kroužek.
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#### Ring

(historical) An old English measure of corn equal to the coomb or half a quarter.
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#### Ring

(computing theory) A hierarchical level of privilege in a computer system, usually at hardware level, used to protect data and functionality (also protection ring).
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#### Ring

(firearms) Either of the pair of clamps used to hold a telescopic sight to a rifle.
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#### Ring

(cartomancy) The twenty-fifth Lenormand card.
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#### Ring

The resonant sound of a bell, or a sound resembling it.
The church bell's ring could be heard the length of the valley.
The ring of hammer on anvil filled the air.
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#### Ring

(figuratively) A pleasant or correct sound.
The name has a nice ring to it.
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#### Ring

(figuratively) A sound or appearance that is characteristic of something.
Her statements in court had a ring of falsehood.
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#### Ring

(colloquial) A telephone call.
I’ll give you a ring when the plane lands.
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#### Ring

Any loud sound; the sound of numerous voices; a sound continued, repeated, or reverberated.
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#### Ring

A chime, or set of bells harmonically tuned.
St Mary's has a ring of eight bells.
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#### Ring

(algebra) An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.
The set of integers, $\mathbb\left\{Z\right\}$, is the prototypical ring.
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#### Ring

(algebra) An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.
The definition of ring without unity allows, for instance, the set $2\mathbb\left\{Z\right\}$ of even integers to be a ring.
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#### Ring

A family of sets that is closed under finite unions and differences.{{cite-book
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#### Ring

(transitive) To enclose or surround.
The inner city was ringed with dingy industrial areas.
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#### Ring

To make an incision around; to girdle; to cut away a circular tract of bark from a tree in order to kill it.
They ringed the trees to make the clearing easier next year.
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#### Ring

(transitive) To attach a ring to, especially for identification.
We managed to ring 22 birds this morning.
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#### Ring

(transitive) To surround or fit with a ring, or as if with a ring.
To ring a pig’s snout
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#### Ring

(falconry) To rise in the air spirally.
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#### Ring

(transitive) To steal and change the identity of (cars) in order to resell them.
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#### Ring

To ride around (a group of animals, especially catle) to keep them milling in one place; hence intransitive, to work as a drover, to muster cattle.
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#### Ring

(intransitive) Of a bell, etc., to produce a resonant sound.
The bells were ringing in the town.
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#### Ring

(transitive) To make (a bell, etc.) produce a resonant sound.
The deliveryman rang the doorbell to drop off a parcel.
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#### Ring

(transitive) To produce (a sound) by ringing.
They rang a Christmas carol on their handbells.
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#### Ring

To produce the sound of a bell or a similar sound.
Whose mobile phone is ringing?
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#### Ring

Of something spoken or written, to appear to be, to seem, to sound.
That does not ring true.
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#### Ring

To telephone (someone).
I will ring you when we arrive.
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#### Ring

(intransitive) to resound, reverberate, echo.
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#### Ring

(intransitive) To produce music with bells.
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#### Ring

(dated) To repeat often, loudly, or earnestly.
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#### Ring

To cause to sound, especially by striking, as a metallic body; as, to ring a bell.
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#### Ring

To make (a sound), as by ringing a bell; to sound.
The shard-borne beetle, with his drowsy hums,Hath rung night's yawning peal.
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#### Ring

To repeat often, loudly, or earnestly.
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#### Ring

To sound, as a bell or other sonorous body, particularly a metallic one.
Now ringen trompes loud and clarion.
Why ring not out the bells?
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#### Ring

To practice making music with bells.
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#### Ring

To sound loud; to resound; to be filled with a ringing or reverberating sound.
With sweeter notes each rising temple rung.
The hall with harp and carol rang.
My ears still ring with noise.
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#### Ring

To continue to sound or vibrate; to resound.
The assertion is still ringing in our ears.
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#### Ring

To be filled with report or talk; as, the whole town rings with his fame.
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#### Ring

To surround with a ring, or as with a ring; to encircle.
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#### Ring

To make a ring around by cutting away the bark; to girdle; as, to ring branches or roots.
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#### Ring

To fit with a ring or with rings, as the fingers, or a swine's snout.
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#### Ring

To rise in the air spirally.
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#### Ring

A sound; especially, the sound of vibrating metals; as, the ring of a bell.
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#### Ring

Any loud sound; the sound of numerous voices; a sound continued, repeated, or reverberated.
The ring of acclamations fresh in his ears.
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#### Ring

A chime, or set of bells harmonically tuned.
As great and tunable a ring of bells as any in the world.
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#### Ring

A circle, or a circular line, or anything in the form of a circular line or hoop.
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#### Ring

Specifically, a circular ornament of gold or other precious material worn on the finger, or attached to the ear, the nose, or some other part of the person; as, a wedding ring.
Upon his thumb he had of gold a ring.
The dearest ring in Venice will I give you.
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#### Ring

A circular area in which races are or run or other sports are performed; an arena.
Place me, O, place me in the dusty ring,Where youthful charioteers contend for glory.
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#### Ring

An inclosed space in which pugilists fight; hence, figuratively, prize fighting.
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#### Ring

A circular group of persons.
And hears the Muses in a ringAye round about Jove's alter sing.
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#### Ring

The plane figure included between the circumferences of two concentric circles.
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#### Ring

An instrument, formerly used for taking the sun's altitude, consisting of a brass ring suspended by a swivel, with a hole at one side through which a solar ray entering indicated the altitude on the graduated inner surface opposite.
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#### Ring

An elastic band partly or wholly encircling the spore cases of ferns. See Illust. of Sporangium.
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#### Ring

A clique; an exclusive combination of persons for a selfish purpose, as to control the market, distribute offices, obtain contracts, etc.
The ruling ring at Constantinople.
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#### Ring

A characteristic sound;
It has the ring of sincerity
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#### Ring

A toroidal shape;
A ring of ships in the harbor
A halo of smoke
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#### Ring

A rigid circular band of metal or wood or other material used for holding or fastening or hanging or pulling;
There was still a rusty iron hoop for tying a horse
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#### Ring

(chemistry) a chain of atoms in a molecule that forms a closed loop
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#### Ring

An association of criminals;
Police tried to break up the gang
A pack of thieves
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#### Ring

The sound of a bell ringing;
The distinctive ring of the church bell
The ringing of the telephone
The tintinnabulation that so volumnously swells from the ringing and the dinging of the bells
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#### Ring

A square platform marked off by ropes in which contestants box or wrestle
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#### Ring

Jewelry consisting of a circlet of precious metal (often set with jewels) worn on the finger;
She had rings on every finger
He noted that she wore a wedding band
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#### Ring

A strip of material attached to the leg of a bird to identify it (as in studies of bird migration)
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#### Ring

Sound loudly and sonorously;
The bells rang
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#### Ring

Ring or echo with sound;
The hall resounded with laughter
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#### Ring

Make (bells) ring, often for the purposes of musical edification;
Ring the bells
My uncle rings every Sunday at the local church
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#### Ring

Be around;
Developments surround the town
The river encircles the village
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#### Ring

Get or try to get into communication (with someone) by telephone;
I tried to call you all night
Take two aspirin and call me in the morning
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#### Ring

Attach a ring to the foot of, in order to identify;
Ring birds
Band the geese to observe their migratory patterns
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