Page "Algebraically closed field" ¶ 5
from Wikipedia

## Some Related Sentences

Since and p
Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.
Since 1990, AIX has served as the primary operating system for the RS / 6000 series ( later renamed IBM eServer pSeries, then IBM System p, and now IBM Power Systems ).
Since the takeover in 2011, NEEP Roma Holding S. p. A. owned all shares Sensi previously hold.
Since the early 20th century it has been commonly accepted that Old Irish Bel ( l ) taine is derived from a Common Celtic * belo-te ( p ) niâ, meaning " bright fire " ( where the element * belo-might be cognate with the English word bale in ' bale-fire ' meaning ' white ' or ' shining '; compare Anglo-Saxon bael, and Lithuanian / Latvian baltas / balts, found in the name of the Baltic ; in Slavic languages byelo or beloye also means ' white ', as in Беларусь ( White Russia or Belarus ) or Бе ́ лое мо ́ ре Sea ).
Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:
~ pp. Since pp is true ( this is Theorem 2. 08, which is proved separately ), then ~ pp must be true.
Since 2 < sup >( q 1 )</ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power x gives 2 < sup >( q 1 ) x </ sup > ≡ 1, and since 2 < sup > p </ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power k gives 2 < sup > kp </ sup > ≡ 1.
Since p is prime q 1 must be a multiple of p. Of course, if the number m = < sup >( q 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.
Since every central subgroup is normal, it follows that every minimal normal subgroup of a finite p-group is central and has order p. Indeed, the socle of a finite p-group is the subgroup of the center consisting of the central elements of order p.
Since lunch is usually served between 2 and 4 p. m., another common time for tapas is weekend days around noon as a means of socializing before proper lunch at home.
* Jackson J. Spielvogel – Western Civilization – Volume II: Since 1500 ( 5th Edition ), p. 401

Since and x
Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.
Since μ is a function of x, we cannot simplify any further directly.
Since the joule is also a Watt-second and the common unit for electricity sales to homes is the kWh ( kilo-Watt-hour ), a kWh is thus 1000 ( kilo ) x 3600 seconds
Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ( other than 1 ) or other function of a variable, equations involving terms such as xy, x < sup > 2 </ sup >, y < sup > 1 / 3 </ sup >, and sin ( x ) are nonlinear.
Since metallic radii are always biggest for the highest coordination number, correction for less dense coordinations involves dividing by x, where 0 < x < 1.
Since y ( t ) is the derivate of x ( t ) we can without loss of generality rewrite it as
Since this force varies with the position of the charge and by Coloumb's Law it is defined at all points in space, is a continuous function of the charge's position ( x, y, z ).
Since the E1 component of nuclear EMP depends on the prompt gamma ray output, which was only 0. 1 % of yield in Starfish Prime but can be 0. 5 % of yield in pure fission weapons of low yield, a 10 kiloton bomb can easily be 5 x 8 % = 40 % as powerful as the 1. 44 megaton Starfish Prime at producing EMP.
The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.
Since a is a limit point of S, W must contain a point x in S. This x S is not covered by the family C, because every U in C is disjoint from V < sub > U </ sub > and hence disjoint from W, which contains x.
Since it lacks a compiler, it cannot be used to produce executable files, although its program source code can still be compiled by a QuickBASIC 4. 5, PDS 7. x or VBDOS 1. 0 compiler, if available.
Since 2008, a set of TCP / IP routines for QuickBASIC 4. x and 7. 1 has revitalized some interest in the software.

Since and is
Since the Supreme Court's decision of that year this is more doubtful ; ;
( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.
Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.
Since attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.
Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.
Since the difficulty of drawing the net is great, we will merely discuss it.
Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.
Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.
Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.
Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.
Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.
Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.
Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.
Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.
Since the apparatus is new, it requires experimentation and changes in technique.
Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.
Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.
Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.
Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

0.433 seconds.