This is the tale of one John Enright, an American who has accidentally killed a man in the prize ring and is now trying to forget about it in a quiet place where he may become a quiet man.

The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

Each fighter has an assigned corner of the ring, where his or her coach, as well as one or more " seconds " may administer to the fighter at the beginning of the fight and between rounds.

During the conversion from straight-chain form to the cyclic form, the carbon atom containing the carbonyl oxygen, called the anomeric carbon, becomes a stereogenic center with two possible configurations: The oxygen atom may take a position either above or below the plane of the ring.

Crocheted fabric is begun by placing a slip-knot loop on the hook ( though other methods, such as a magic ring or simple folding over of the yarn may be used ), pulling another loop through the first loop, and repeating this process to create a chain of a suitable length.

Secondary volcanic vents may form above the ring fracture.

" Slap style " may have influenced electric bass guitar players who, from the mid-sixties ( particularly Larry Graham of Sly and the Family Stone ), developed a technique called slap and pop that used the thumb of the plucking hand to hit the string, making a slapping sound but still letting the note ring, and the index or middle finger of the plucking hand to pull the string back so it hits the fretboard, achieving the pop sound described above.

As a ring, a field may be classified as a specific type of integral domain, and can be characterized by the following ( not exhaustive ) chain of class inclusions:

As in the simple cases above, one may enumerate all distinct four-colorings of the ring ; any coloring that can be extended without modification to a coloring of the configuration is called initially good.

An example of such a finite field is the ring Z / pZ, which is essentially the set of integers from 0 to p − 1 with integer addition and multiplication modulo p. It is also sometimes denoted Z < sub > p </ sub >, but within some areas of mathematics, particularly number theory, this may cause confusion because the same notation Z < sub > p </ sub > is used for the ring of p-adic integers.

Corresponding to the Bezout property we may, in any commutative ring, consider the collection of elements of the form pa + qb, where p and q range over the ring.

Even though the set may be the same, the same function might be a homomorphism, say, in group theory ( sets with a single operation ) but not in ring theory ( sets with two related operations ), because it fails to preserve the additional operation that ring theory considers.

Clement of Alexandria, in his Paedagogus ( The Pedagogue ) 3. 59. 2-3. 60, writes that Christians may wear a seal ring for the sealing of documents, and he specifies permissible depictions: " And let our seals be either a dove, or a fish, or a ship scudding before the wind, or a musical lyre, which Polycrates used, or a ship's anchor, which Seleucus got engraved as a device ; and if there be one fishing, he will remember the apostle, and the children drawn out of the water.

Thus, for example, two objects may be group isomorphic without being ring isomorphic, since the latter isomorphism selects the additional structure of the multiplicative operator.

One may define a partial order on the idempotents of a ring as follows: if a and b are idempotents, we write if and only if.

One may consider the ring of integers mod n, where n is squarefree.

This same construction may be carried out if the A < sub > i </ sub >' s are sets, rings, modules ( over a fixed ring ), algebras ( over a fixed field ), etc., and the homomorphisms are homomorphisms in the corresponding category.

The large and many holes in lacy knitting makes it extremely elastic ; for example, some Shetland " wedding-ring " shawls are so fine that they may be drawn through a wedding ring.

Emergency insertion of a copper IUC is significantly more effective than the use of ECPs, reducing the risk of pregnancy following unprotected intercourse by more than 99 %.< sup > 2, 3 </ sup > This very high level of effectiveness implies that emergency insertion of a copper IUC must prevent some pregnancies after fertilization. Emergency contraceptive pillsTo make an informed choice, women must know that ECPs — like the birth control pill, patch, ring, shot, and implant ,< sup > 76 </ sup > and even like breastfeeding < sup > 77 </ sup >— prevent pregnancy primarily by delaying or inhibiting ovulation and inhibiting fertilization, but may at times inhibit implantation of a fertilized egg in the endometrium.

For example, the aldohexose glucose may form a hemiacetal linkage between the hydroxyl on carbon 1 and the oxygen on carbon 4, yielding a molecule with a 5-membered ring, called glucofuranose.

As the cap expands, the veil breaks, and remnants of the partial veil may remain as a ring, or annulus, around the middle of the stalk or as fragments hanging from the margin of the cap.

When you and your dog step into the Junior ring, it should be just what the dog wants to do as much as what you want him to do.

Although the manufacturer committed to re-do the broken parts, Gaudí liked the aesthetic of the broken masonry and asked that the pieces be stuck to the main structure with lime mortar and held in with a brass ring.

Let R be a fixed commutative ring.

* Any ring A can be considered as a Z-algebra in a unique way.

The greater the recoil a weapon on an AFV is, the larger the turret ring needs to be.

Several related flagellates, such as Perkinsus and Colpodella have structures similar to the polar ring and were formerly included here, but most appear to be closer relatives of the dinoflagellates.

For bridged alkenes, the Bredt's rule states that a double bond cannot be placed at the bridgehead of a bridged ring system, unless the rings are large enough.

In Thomson's model, electrons were free to rotate in rings which were further stabilized by interactions between the electrons, and spectra were to be accounted for by energy differences of different ring orbits.

The bone ring was designed to break after impact so that the shaft could be used again for another kill.

There were twelve rules in all, and they specified that fights should be " a fair stand-up boxing match " in a 24-foot-square or similar ring.

The definition works without any changes if instead of vector spaces over a field F, we use modules over a commutative ring R. It also can be easily generalized to n-ary functions, where the proper term is multilinear.

Let A be a unital commutative Banach algebra over C. Since A is then a commutative ring with unit, every non-invertible element of A belongs to some maximal ideal of A.

Descartes recognized that there would be a real difference, however, between a situation in which a body with movable parts and originally at rest with respect to a surrounding ring was itself accelerated to a certain angular velocity with respect to the ring, and another situation in which the surrounding ring was given a contrary acceleration with respect to the central object.

With sole regard to the central object and the surrounding ring, the motions would be indistinguishable from each other assuming that both the central object and the surrounding ring were absolutely rigid objects.

When there are no enemy discs on the board, many ( but not all ) rules also state that a player must shoot for the centre of the board, and a shot disc must finish either completely inside the 15-point guarded ring line, or ( depending on the specifics of the rules ) be inside or touching this line.

Impact craters are not to be confused with other landforms that in some cases appear similar, including calderas and ring dikes.

If a second compression test is performed shortly thereafter, and the new reading is much higher, it would be the ring seal that is problematic, whereas if the compression test pressure observed remains low, it is a valve sealing ( or more rarely head gasket, or breakthrough piston or rarer still cylinder wall damage ) issue.

The heme group is a highly-conjugated ring system ( which allows its electrons to be very mobile ) surrounding a metal ion, which readily interconverts between the oxidation states.

If A is a fixed element of a ring ℜ, the first additional relation can also be interpreted as a Leibniz rule for the map given by B ↦.

* The bottom half contains the nationality and birth number and has a hole so the broken-off half can be hung on a ring.