A ring R (with 1) is a set equipped with two binary operations usually denoted by addition (+) and multiplication and an element 1 in R such that:
• (R,+) is an abelian group
• a(bc)=(ab)c for all a,b,c in R (associativity)
• a(b+c)=ab+ac and (b+c)a=ba+ca for all a,b,c in R (distributivity)
• 1a=a1=a for all a in R (identity)

An example of of a commutative ring is the ring of integers Z={...,-1,0,1,2,...} with the usual addition and multiplication.

An example of a noncommutative ring is the ring of all nxn matrices with complex entries.

Mathematicians who contributed to ring theory include David Hilbert and Emmy Noether

Rings turn up naturally in lots of places in mathematical physics.

The Weyl algebra is an interesting noncommutative ring.

In NetHack, a ring is a magical item that (usually) bestows its effects continuously -- they do not expend charges, nor are they invoked. You can only wear two rings at a time (one on each hand). Each ring worn increases the rate at which you get hungry by about 5%. A ring of hunger will increase the rate by 50% (as will a ring of regeneration). Some rings (like the ring of adornment) are simply not worth wearing due to this effect.

Being blessed increases the effectiveness of certain rings. A cursed ring cannot be removed normally, in addition to possible other effects as noted -- this is extremely problematic with the ring of levitation and the ring of hunger, among others.

Rings can be eaten if you are polymorphed into a petrivore or metallivore. Eating a ring has a 1/3 chance of bestowing the ring's power as an intrinsic, if practical (ring of poison resistance); otherwise not (ring of levitation). In all cases the ring is lost. Some rings can be affected by the stone to flesh spell. This will transform it into a "meat ring", which is edible as food but loses all magical power.

NetHack rings include:

Ring is a science fiction novel by Stephen Baxter. A weathly cult, Superet, funds a probe to investigate the sun, hopefully to discover why the number of neutrinos it is releasing is so low. Lieserl, a human, is engineered to provide a conscious in-situ control of the probe. She discovers the reason for the lack of neutrinos, and it's a plague that is destroying all the stars.

An expedition is mounted to use relativistic travel to pass 5,000,000 years into the future to investigate. They return to find the remnants of vast engineering projects, and the signs that humans fought and lost a war against the Xeelee, the rulers of the universe. Talking with Leiserl who has observed the events of the past 5,000,000 years, leads them to investigate the Great Attractor, rumuored to be the greatest engineering project of the Xeelee; the lords of the universe. The Xeelee's project offers them the only hope as the stars fade and die.....

Again Stephen Baxter puts the science into science fiction, and proves he can think further and deeper than most. A book of vast scope and vision, and one that can be re-read many times!

The different privilege levels on an Intel processor when running in protected mode are also called "rings". There are four rings, 0 to 3, with lower number meaning more privileges.

Ring 0 - Operating system kernel
Ring 1 - Device drivers. Not always used.
Ring 2 - Device drivers. Not always used.
Ring 3 - Application programs

Device drivers often run in ring 0, instead of in ring 2 or 3.

Some instructions can only be executed at ring 0, for example LGDT (Load GDT register). Access to memory segments and pages can also be limited by the privilege level. For example, a memory page marked with "Supervisor Mode" can only be accessed from ring 0, 1 and 2.

RING is a film by the Japanese director, Hideo Nakata. And it's subtitled, rather than dubbed, and features many fine actors, such as Matsushima Nanako and Nakatani Miki.

And it's scary. Pant-wetting scary. Psychological scary.

Don't expect flying organs or suddenly finding your sister's one of them. Don't expect much, because it is very surprising and unnerving in places.

The basic plot is simple: reporter Reiko Asakawa, played by actress Matsushima Nanako, is investigating a cursed video; Whoever watches it, dies. Soon after, her niece dies for no known reason with a bizzare expression on her face. She then investigates even more, and finds the tape. She then puts it on, and watches it*. And the tape is real. With but seven days alive, she must find the answers of how to stop the video.

Based on a book by Suzuki Koji, this masterpeice is one of the best films of all time. Made for only 1.2 million dollars, it's small budget- and has been a hit in many countries, including China, Japan, and Singapore. Ring even smashed the box-office records in Japan on release.

Ring spawned a LOT in its path- it is, after all, Japanese, and as anyone who's seen what the Japanese are like with AnimÃ© will know- once the Japanese like something, they LIKE it.

Products include:
-A sequel, with another in production (Ring 2 and 3)
-A prequal (Ring 0)
-2 television series
-Manga,
-Other books
-Photo-booths where you have your picture taken with the ghost from Ring.
-Rasen, a sequel made by a different company to the original... which is very, very poor, unfortunately, and has many changes in plot. Ignore this one, watch Ring 2. However, the book version of Rasen is pretty good I've been told.

Ring, Ring 2, and Ring 0 are already on DVD from Tartan Video in Britain and bootleg copies in US. A translated version of the film is meant to be coming to the US, and the English translation of the book has just appeared in US.

Many theories are out there behind so much of the plot- as it has had so much about it including novels and such, all of which seem to echo each other in some way, the ideas behind the plot become very interesting... one I have seen is at http://www.somrux.com/ringworld; It brings a lot of theories and questions and answers to some.

If you EVER see this film ANYWHERE, see it. You must.
And after watching, you'll never put a strange video on again.

*One of the stupidest things anyone could ever do, really.

Ring (?), v. t. [imp. Rang (?) or Rung (); p. p. Rung; p. pr. & vb. n. Ringing.] [AS. hringan; akin to Icel. hringja, Sw. ringa, Dan. ringe, OD. ringhen, ringkelen. &root;19.]

1.

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

2.

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. Shak.

3.

To repeat often, loudly, or earnestly.

To ring a peal, to ring a set of changes on a chime of bells. -- To ring the changes upon. See under Change. -- To ring in or out, to usher, attend on, or celebrate, by the ringing of bells; as, to ring out the old year and ring in the new. Tennyson. -- To ring the bells backward, to sound the chimes, reversing the common order; -- formerly done as a signal of alarm or danger. Sir W. Scott.

Ring, v. i.

1.

To sound, as a bell or other sonorous body, particularly a metallic one.

Now ringen trompes loud and clarion. Chaucer.

Why ring not out the bells? Shak.

2.

To practice making music with bells.

Holder.

3.

To sound loud; to resound; to be filled with a inging or reverberating sound.

With sweeter notes each rising temple rung. Pope.

The hall with harp and carol rang. Tennyson.

My ears still ring with noise. Dryden.

4.

To continue to sound or vibrate; to resound.

The assertion is still ringing in our ears. Burke.

5.

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

Ring, n.

1.

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

2.

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

The ring of acclamations fresh in his ears. Bacon

3.

A chime, or set of bells harmonically tuned.

As great and tunable a ring of bells as any in the world. Fuller.

Ring (?), n. [AS. hring, hrinc; akin to Fries. hring, D. & G. ring, OHG. ring, hring, Icel. hringr, DAn. & SW. ring; cf. Russ. krug'. Cf. Harangue, Rank a row,Rink.]

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

2.

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. Chaucer.

The dearest ring in Venice will I give you. Shak.

3.

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 contened for glory. E. Smith.

4.

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

"The road was an institution, the ring was an institution."

Thackeray.

5.

A circular group of persons.

And hears the Muses in a Aye round about Jove's alter sing. Milton.

6. Geom. (a)

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

(b)

The solid generated by the revolution of a circle, or other figure, about an exterior straight line (as an axis) lying in the same plane as the circle or other figure.

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.

8. Bot.

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

9.

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. E. A. Freeman.

Ring armor, armor composed of rings of metal. See Ring mail, below, and Chain mail, under Chain. -- Ring blackbird Zool., the ring ousel. -- Ring canal Zool., the circular water tube which surrounds the esophagus of echinoderms. -- Ring dotterel, or Ringed dotterel. Zool. See Dotterel, and Illust. of Pressiroster. -- Ring dropper, a sharper who pretends to have found a ring (dropped by himself), and tries to induce another to buy it as valuable, it being worthless. -- Ring fence. See under Fence. -- Ring finger, the third finger of the left hand, or the next the little finger, on which the ring is placed in marriage. -- Ring formula Chem., a graphic formula in the shape of a closed ring, as in the case of benzene, pyridine, etc. See Illust. under Benzene. -- Ring mail, a kind of mail made of small steel rings sewed upon a garment of leather or of cloth. -- Ring micrometer. Astron. See Circular micrometer, under Micrometer. -- Saturn's rings. See Saturn. -- Ring ousel. Zool. See Ousel. -- Ring parrot Zool., any one of several species of Old World parrakeets having a red ring around the neck, especially Palaeornis torquatus, common in India, and P. Alexandri of Java. -- Ring plover. Zool. (a) The ringed dotterel. (b) Any one of several small American plovers having a dark ring around the neck, as the semipalmated plover (Aegialitis semipalmata). -- Ring snake Zool., a small harmless American snake (Diadophis punctatus) having a white ring around the neck. The back is ash-colored, or sage green, the belly of an orange red. -- Ring stopper. Naut. See under Stopper. -- Ring thrush Zool., the ring ousel. -- The prize ring, the ring in which prize fighters contend; prize fighters, collectively. -- The ring. (a) The body of sporting men who bet on horse races. [Eng.] (b) The prize ring.

Ring, v. t. [imp. & p. p. Ringed (?); p. pr. & vb. n. Ringing.]

1.

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

"Ring these fingers."

Shak.

2. Hort.

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

3.

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

Ring, v. i. Falconry

To rise in the air spirally.

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