Then the archbishops and bishops approached and kissed his feet.

Then R / I is a ring with unity, ( respectively, R / A is a finitely generated module ), and so the above theorems can be applied to the quotient to conclude that there is a maximal ideal ( respectively maximal right ideal ) of R containing I ( respectively, A ).

Then both step back into the ring, squat facing each other, clap their hands, then spread them wide ( traditionally to show they have no weapons ).

Let R be a Noetherian ring and let I be an ideal of R. Then I may be written as the intersection of finitely many primary ideals with distinct radicals ; that is:

Then R (( G )) is the ring of formal power series on G ; because of the condition that the indexing set be well-ordered the product is well-defined, and we of course assume that two elements which differ by zero are the same.

Then, after proving that the Draques are members of the crime ring, Nick reveals the identity of the leader of the gang: Dr. Bruce Clayworth.

The other class of Dedekind rings which is arguably of equal importance comes from geometry: let C be a nonsingular geometrically integral affine algebraic curve over a field k. Then the coordinate ring k of regular functions on C is a Dedekind domain.

Then when he did, the rowdy tactics got under way and ended only when either both were sprawled on the canvas still wrestling each other, or the referee was outside the ring trying pull the boys apart or both fighters and official were entangled in a pretzel formation on the ring floor.

Then the ring is pushed by hand onto the base of the erect penis before releasing the vacuum.

: Then taking your ring and pentacle, put the ring on the little finger of your right hand ; hang the pentacle round thy neck ; ( Note, the pentacle may be either wrote on clean virgin parchment, or engraven on a square plate of silver and suspended from thy neck to the breast )....

Then the bells will ring so merrily

Then Walcott looked outside the ring ( presumably to the ringside count keeper ) as Ali and Liston went at each other before Walcott instructed them to keep on fighting, then Walcott approached the fighters and abruptly stopped the fight.

* Let k be the coordinate ring of the variety V. Then the dimension of V is the transcendence degree of the field of fractions of k over k.

Let V be an algebraic set defined as the set of the common zeros of an ideal I in a polynomial ring over a field K, and let A = R / I be the algebra of the polynomials over V. Then the dimension of V is:

Then one checks that these two functions are in fact both ring homomorphisms.

Then it is possible to have zero divisors in the ring of regular functions, and consequently the fraction field no longer exists.

Then, during a match between Hall, Nash, Sting and The Giant ( who had recently rejoined the nWo after being kicked out two years prior ), Hall turned on Nash by hitting him with his tag team title belt and leaving the ring.

More precisely, let F be a field, and let F be the ring of polynomials in one variable, X, with coefficients in F. Then each f < sub > i </ sub > lies in F. ∂< sub > X </ sub > is the derivative with respect to X.

In symbols, let A be a Noetherian local ring with maximal ideal m, and suppose a < sub > 1 </ sub >, ..., a < sub > n </ sub > is a minimal set of generators of m. Then in general n ≥ dim A, and A is defined to be regular if n = dim A.

Suppose that R is an algebra over the field C of complex numbers and M = N is a finite-dimensional simple module over R. Then Schur's lemma says that the endomorphism ring of the module M is a division ring ; this division ring contains C in its center, is finite-dimensional over C and is therefore equal to C. Thus the endomorphism ring of the module M is " as small as possible ".

Then, with staring eyes and lips drawn thin, Miriam said to the young woman, `` You are ugly -- uglier than you used to be, and you were always very ugly.

Then, all but blind, he said there was nothing in Back to Methuselah --, -- `` G.B.S. ought to have known that '', -- and `` I look at my bookshelves despairingly, knowing that I can have nothing more to do with them ''.

Then Jennie closed her eyes, stretched forth her arms, and said: `` Take my hand, Louise ; ;

Then, they said General Burnside was going to jump over his horse's head ; ;

Then he asked to use the phone and called Brian Thayer, who said that he was just leaving to keep a lunch date but would be home by two o'clock.

Then he said, `` Never noticed it before I mean, when she was dressed but for a woman her age, Julia had a real fine figure ''.

I said quietly, gaining nerve, ready to ask any question at all, no matter how intimate, ready to be rebuffed, `` Then why did she leave Israel??

Then she said, `` Allons '', and we got up and went to my hotel without another word.

Then Frankie said: `` What are you gonna do ''??

Then, he said, `` Unfortunately, only one lamechian linguist exists, and he is too old for this expedition.

Then, a little later, Shilkret discovered there was no one to play the brief celesta solo during the slow section, so he hastily asked Gershwin if he might play the solo ; Gershwin said he could and so he briefly participated in the actual recording.

: Then King Pasenadi Kosala said to the Blessed One, " Lord, what is the name of this monk?

Then they suggested Mu ' awiya ( founder of the Umayyad Caliphate ), but the Caliph again said no.

Then the Lord said, " Rise and anoint him ; this is the one.

Then again, who said bad taste was easy?

Then he said " I'm fining everyone in this courtroom fifty cents for living in a city where a person has to steal bread in order to eat!

Then he laughed, pulled a necklace of Spanish gold from around his neck and said " Our voyage is made, lads!

Then, Gödel defined essences: if x is an object in some world, then the property P is said to be an essence of x if P ( x ) is true in that world and if P entails all other properties that x has in that world.

Then came an even more shocking confession: according to the CIA document, al-Faruq said two senior al-Qaeda officials, Abu Zubaydah and Ibn al-Shaykh al-Libi, had ordered him to ' plan large-scale attacks against U. S. interests in Indonesia, Malaysia, ( the ) Philippines, Singapore, Thailand, Taiwan, Vietnam and Cambodia.

“ And that Christ being Lord, and God the Son of God, and appearing formerly in power as Man, and Angel, and in the glory of fire as at the bush, so also was manifested at the judgment executed on Sodom, has been demonstrated fully by what has been said .” Then I repeated once more all that I had previously quoted from Exodus, about the vision in the bush, and the naming of Joshua ( Jesus ), and continued: “ And do not suppose, sirs, that I am speaking superfluously when I repeat these words frequently: but it is because I know that some wish to anticipate these remarks, and to say that the power sent from the Father of all which appeared to Moses, or to Abraham, or to Jacob, is called an Angel because He came to men ( for by Him the commands of the Father have been proclaimed to men ); is called Glory, because He appears in a vision sometimes that cannot be borne ; is called a Man, and a human being, because He appears arrayed in such forms as the Father pleases ; and they call Him the Word, because He carries tidings from the Father to men: but maintain that this power is indivisible and inseparable from the Father, just as they say that the light of the sun on earth is indivisible and inseparable from the sun in the heavens ; as when it sinks, the light sinks along with it ; so the Father, when He chooses, say they, causes His power to spring forth, and when He chooses, He makes it return to Himself.

Ludlow stated in early January, 1660 when in conversation with several key officers of the army: ' Then ,' said Capt.

Then, in October 2004, the International Monetary Fund and the World Bank said they would write off $ 2 billion in debt — almost half Madagascar's total debt.

Then Rachel said to Leah, Give me, I pray thee, of thy son's mandrakes.

* He said to them ..." Then he said unto them, O fools, and slow of heart to believe all that the prophets have spoken: Ought not Christ to have suffered these things, and to enter into his glory?