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.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.

For example, the proof that the column rank of a matrix over a field equals its row rank yields for matrices over division rings only that the left column rank equals its right row rank: it does not make sense to speak about the rank of a matrix over a division ring.

For example, a benzene ring or double bond in conjugation with the carbonyl will bring the wavenumber down about 30 cm < sup >− 1 </ sup >.

* K, the ring of polynomials over a field K. For each nonzero polynomial P, define f ( P ) to be the degree of P.

* K < nowiki ></ nowiki > X < nowiki ></ nowiki >, the ring of formal power series over the field K. For each nonzero power series P, define f ( P ) as the degree of the smallest power of X occurring in P. In particular, for two nonzero power series P and Q, f ( P )≤ f ( Q ) iff P divides Q.

For other examples of quotient objects, see quotient ring, quotient space ( linear algebra ), quotient space ( topology ), and quotient set.

For example, a ring possesses both addition and multiplication, and a homomorphism from the ring to the ring is a function such that

For example, a Hall sensor integrated into a ferrite ring ( as shown ) can reduce the detection of stray fields by a factor of 100 or better ( as the external magnetic fields cancel across the ring, giving no residual magnetic flux ).

For example, most network cards implement transmit and receive ring buffers, interrupt rate limiting, and hardware flow control.

For the end, two finalists squared off in a boxing ring for a two-minute round to declare the champion.

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.

For example, in the ring, we have

For instance, electrons and positive ions trapped in the dipole-like field near the Earth tend to circulate around the magnetic axis of the dipole ( the line connecting the magnetic poles ) in a ring around the Earth, without gaining or losing energy ( this is known as Guiding center motion ).

For example, hemoglobin and myoglobin contain an iron center coordinated to the nitrogen atoms of a porphyrin ring ; magnesium is the center of a chlorin ring in chlorophyll.

For instance, the ring ( in fact field ) of complex numbers, which can be constructed from the polynomial ring R over the real numbers by factoring out the ideal of multiples of the polynomial.

For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

For safety, the ropes are padded at the turnbuckles and cushioned mats surround the floor outside the ring.

For organization and ease of reference here, the relevant major terrorist attacks are listed by date below, with a brief summary for each, identifying the terror cells most directly responsible for the attack.

For example, on 31 January 2006, Tony Blair's Government was defeated over certain aspects of proposals to outlaw religious hatred, and, on 9 November 2005, was defeated over plans which would have allowed police to detain terror suspects for up to 90 days without charge.

" For Big Nurse in One Flew Over the Cuckoo's Nest, it was a tool of terror, and, in the public mind, shock therapy has retained the tarnished image given it by Ken Kesey's novel: dangerous, inhumane and overused ".

A plaque commemorating the bombing was unveiled, stating " For reasons known only to the British, the hotel was not evacuated .” The British Ambassador in Tel Aviv and the Consul-General in Jerusalem protested, saying " We do not think that it is right for an act of terrorism, which led to the loss of many lives, to be commemorated ," and wrote to the Mayor of Jerusalem that such an act of terror could not be honoured, even if it was preceded by a warning.

For the reign of terror which followed the downfall of the Parthenopaean Republic, five months later, Acton has been held responsible.

: For Greece is already entirely obedient to you, and will remain so: the Achaeans from genuine affection ; the Aetolians from the terror which their disasters in the present war have inspired them.

Paul's letter to Roman Christians declares " For rulers hold no terror for those who do right, but for those who do wrong.

For example, the dance of the Furies, so represented, would create complete terror among those who witnessed them.

For many months in 1942, the OUN-B was not able to control the situation in Volhynia, where in addition to Soviet partisans, many independent Ukrainian self-defense groups started to form in response to the growth of German terror.

For instance, Dekkushev acknowledged that he knew the explosives he transported were to be used for an act of terror.

For Mary Ashley has been marked for death by the world's most proficient and mysterious assassin, and plunged into a nightmare of espionage, kidnapping and terror.

For example, in Hamlet, " Hamlet's encounter with the Ghost becomes for Walpole a template for terror ".

In 1951, during the darkest period of terror, Kott published an ideological manifesto about the role of theatre, entitled " O teatr godny naszej epoki " ( For theatre worthy of our times ), in which he demanded a " new " theatre subservient to the Party and its ideology.

For example, the Jemaah Islamiyah ( JI ) terror group is the latest anti-Pancasila manifestation.

For example, the song " Homeland Security " lampooned exaggerated terror threats, and " John Ashcroft and The Spirit of Justice " comically mocked John Ashcroft's prudishness over the Spirit of Justice statue.

For cold-drakes that have never before felt pain, the combination of pain and heat is enough to cause disorientation, delirium, and an infant-like blurring of the vision, allowing an Empath to use their Gift to delude the cold-drake into momentarily thinking they are larger and vastly more powerful, this in turn is the only known means by whence an Empath may instill terror in a cold-drake sufficient to make it flee.

For Haydn, writing the Mass in the late summer of 1798, the mood in Eisenstadt was one of foreboding, to the point of terror, and this is what we hear as the great work opens: Haydn chose to write the opening movement in D minor.

For countless ages, primitive man has worshipped the fire-god in dumb terror.

: For Greece is already entirely obedient to you, and will remain so: the Achaeans from genuine affection ; the Aetolians from the terror which their disasters in the present war have inspired them.

For a long time, Kerala was considered as a terror free state and model of tolerance and prosperity.

For the first time it attacked Khomeini directly as responsible for repression and a reign of terror.

For years, the park's racetracks have wreaked terror on its participants in ways too gruesome to describe on regulated television.

For example, Esther Griggs in 1858 threw her child out of a first floor window believing that the house was on fire, whilst having a night terror ( Walker, 1968 ).

Fuel For Truth ( FFT ) is a non for profit organization that seeks to " equip young Americans with the basic facts and skills necessary to advocate to young adults, to increase support for Israel in her battle against radical Islamic terror ".