* Generating set of an ideal ( ring theory ):

In 1930, England captain Douglas Jardine, together with Nottinghamshire's captain Arthur Carr and his bowlers Harold Larwood and Bill Voce, developed a variant of leg theory in which the bowlers bowled fast, short-pitched balls that would rise into the batsman's body, together with a heavily stacked ring of close fielders on the leg side.

His mathematical specialties were noncommutative ring theory and computational algebra and its applications, including automated theorem proving in geometry.

* Conductor ( ring theory ), an ideal of a ring that measures how far it is from being integrally closed

There are different definitions used in group theory and ring theory.

In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.

Another definition of the GCD is helpful in advanced mathematics, particularly ring theory.

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.

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.

In the language of category theory it is a morphism in the category of modules over a given ring.

In ring theory, the notion of number is generally replaced with that of ideal.

* Radical of a ring, in ring theory, a radical of a ring is an ideal of " bad " elements of the ring

In the α anomer, the-OH substituent on the anomeric carbon rests on the opposite side ( trans ) of the ring from the CH < sub > 2 </ sub > OH side branch.

In algebra ( which is a branch of mathematics ), a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers.

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.

In the branch of mathematics known as abstract algebra, a ring is an algebraic concept abstracting and generalizing the algebraic structure of the integers, specifically the two operations of addition and multiplication.

The biosynthesis of cephems branch off at isopenicillin N by an oxidative ring expansion to the cephem core.

In mathematics, more specifically ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is an ideal which consists of those elements in R which annihilate all simple right R-modules.

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

From the nerve ring, five nerves radiate underneath the radial canals of the water vascular system, and branch into numerous finer nerves to innervate the tube feet, spines, and pedicellariae.

In ring theory, a branch of abstract algebra, a principal ideal is an ideal I in a ring R that is generated by a single element a of R.

Fruiting spurs are specialized twigs that generally branch off the sides of branches and leading twigs, and are stubby and slow-growing, with many annular ring markings from seasons past.

In ring theory, a branch of modern algebra, a quotient ring, also known as factor ring or residue class ring, is a construction quite similar to the factor groups of group theory and the quotient spaces of linear algebra.

From this ring, nerves branch forwards to innervate the mouth and subradula, while two pairs of main nerve cords run back through the body.

In commutative ring theory, a branch of mathematics, the radical of an ideal I is an ideal such that an element x is in the radical if some power of x is in I.

In ring theory, a branch of mathematics, a radical of a ring is an ideal of " bad " elements of the ring.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

In mathematics, specifically commutative algebra, Hilbert's basis theorem states that every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated.

* Module ( mathematics ) over a ring, a generalization of vector spaces

In mathematics, it is possible to combine several rings into one large product ring.

In mathematics, specifically in ring theory, the simple modules over a ring R are the ( left or right ) modules over R which have no non-zero proper submodules.

In mathematics, more specifically in ring theory, a maximal ideal is an ideal which is maximal ( with respect to set inclusion ) amongst all proper ideals.

In mathematics, a Boolean ring R is a ring for which x < sup > 2 </ sup > = x for all x in R ; that is, R consists only of idempotent elements.

In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non-empty set of ideals has a maximal element.

* 1966 – Lilian Garcia, Spanish-American singer and ring announcer

He had introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and given a proof of the Riemann – Roch theorem with them ( a version appeared in his Basic Number Theory in 1967 ).

Within 4 – 5 days the inflammation and the concomitant dead brain tissue are surrounded with a capsule, which gives the lesion the famous ring-enhancing lesion appearance on CT examination with contrast ( since intravenously applied contrast material can not pass through the capsule, it is collected around the lesion and looks as a ring surrounding the relatively dark lesion ).

* Ring counter – formed by a shift register with feedback connection in a ring

* Johnson counter – a twisted ring counter

** – ring

Two further water bodies – the Grand Canal on the southside and the Royal Canal on the northside – ring the inner city on their way to the west and the River Shannon.

* 1942 – The Federal Bureau of Investigation ( FBI ) convicts 33 members of a German spy ring headed by Fritz Joubert Duquesne in the largest espionage case in United States history — the Duquesne Spy Ring.

If the man wearing a gold ring is fighting a battle on land the mention of the sea will have no relevance to his situation at all and does not contribute to the picture of the battle being described ” ( Faulkes ( 1997 ), pp. 8 – 9 ).

# The ring current field, carried by plasma trapped in the dipole-like field around Earth, typically at distances 3 – 8 R < SUB > E </ SUB > ( less during large storms ).

The magnetic disturbance may decay within 1 – 3 days as many ions are removed by charge exchange, but the higher energies of the ring current can persist much longer.

* 1944 – Soviet spy Richard Sorge, a half-Russian, half-German World War I veteran, is hanged by his Japanese captors along with 34 of his ring.

* 1987 – Ariane Andrew, American professional wrestler, manager and ring announcer

Only proline differs from this basic structure as it contains an unusual ring to the N-end amine group, which forces the CO – NH amide moiety into a fixed conformation.

The prime ideals of the ring of integers are the ideals ( 0 ), ( 2 ), ( 3 ), ( 5 ), ( 7 ), ( 11 ), … The fundamental theorem of arithmetic generalizes to the Lasker – Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

Yahalom is usually translated by the Septuagint as an " onyx ", but sometimes as " beryl " or as " jasper "; onyx only started being mined after the Septuagint was written, so the Septuagint's term " onyx " probably does not mean onyx – onyx is originally an Assyrian word meaning ring, and so could refer to anything used for making rings.

Aos sí are sometimes seen as fierce guardians of their abodes – whether a fairy hill, a fairy ring, a special tree ( often a hawthorn ) or a particular loch or wood.