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Conversely, the valuation on a discrete valuation ring can be extended to a valuation on the quotient field giving a discrete valued field, whose associated discrete valuation ring is just.
Some Related Sentences
Conversely and on
Conversely, a standard line on which voice service has been unsubscribed ( such as an ADSL dry loop ) may still accept calls to the 958 test exchange but not allow calls to standard numbers.
Conversely, paintings which came out of his workshop that were not necessarily physically worked on by Cuyp but merely overseen by him technically, were marked with A. C. to show that it was his instruction which saw the paintings ’ completion.
Conversely, modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.
Conversely, Fleet Captain Honoré Ganteaume later reported the cause as an explosion on the quarterdeck, preceded by a series of minor fires on the main deck among the ship's boats.
* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.
Conversely, if ƒ: C → C is a function which is differentiable when regarded as a function on R < sup > 2 </ sup >, then ƒ is complex differentiable if and only if the Cauchy – Riemann equations hold.
Conversely the car is stopped by releasing pressure on the cable ( with or without completely detaching ) and applying the brakes.
Conversely, every point on the line can be interpreted as a number in an ordered continuum which includes the real numbers.
Conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earth's surface ( except exactly on the equator ).
Conversely, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.
Conversely, Derek Bickerton and others argue that the advent of abstract words provided a mental basis for analyzing higher-order relations, and that any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language.
" Conversely, Pat Graham of Chicago Reader disliked the mix of horror and comedy, writing in his review that " The pop-up humor and smirkiness suggest Raimi's aspiring to the fashionable company of the brothers Coen, though on the basis of this strained effort I'd say he's overshot the mark.
Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f ( x ) both times.
Conversely, the blood vessels in the lower legs are under great pressure ( because of the weight of fluid pressing down on them ).
Conversely on occasions he attracted criticism for dogmatically pursuing schemes favoured by the right of his party, notably the privatisation of British Rail, and for closing down most of the coal industry in advance of privatisation.
Conversely, some areas which were merely roadside suburbs in the 1950s are now valuable urban land on which original structures are being removed through gentrification and the land used for other purposes.
Conversely, the cultural divergence at the border became sharper: in theory, a uniform French identity extends from the Atlantic coast to the Rhine, and on the other bank of the Rhine, a uniform German identity begins.
Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation.
Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and you can expect to win less money on average than it costs to call the bet.
Conversely, from a partial order on a partition of a set S one can construct a preorder on S. There is a 1-to-1 correspondence between preorders and pairs ( partition, partial order ).
Conversely and discrete
Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.
Conversely, when one wants to compute an arbitrary number ( N ) of discrete samples of one cycle of a continuous DTFT, it can be done by computing the relatively simple DFT of s < sub > N </ sub >, as defined above.
") Conversely, " fire " is frequently used as a mass noun, but " a fire " refers to a discrete entity.
Conversely and ring
Conversely, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y.
It is a fact that the ring is a principal ideal ring ; that is, for any ideal I in, there exists an integer n in I such that every element of I is a multiple of n. Conversely, the set of all multiples of an arbitrary integer n is necessarily an ideal, and is usually denoted by ( n ).
This ring is the endomorphism ring of A. Conversely, every ring ( with identity ) is the endomorphism ring of some object in some preadditive category.
Conversely, given any ring, we can form a category by taking objects A < sub > n </ sub > indexed by the set of natural numbers ( including zero ) and letting the hom-set of morphisms from to be the set of-by-matrices over, and where composition is given by matrix multiplication.
Conversely, given a Boolean ring R, we define the join operation by a ' b = a + b + ab, and the meet operation as multiplication.
Conversely, if this identity holds in a ring R for all pairs of elements a and b of the ring, then R is commutative.
Conversely, Haystacks was an accomplished wrestler, and he consequently took the majority of the decisions, many by countout ( as Humphrey often could not get himself back into the ring by the count of 20 ).
Statement 4 then implies that a basis of M / mM lifts to a minimal set of generators of M. Conversely, every minimal set of generators of M is obtained in this way, and any two such sets of generators are related by an invertible matrix with entries in the ring.
If f is unramified at a point x, then f is quasi-finite at x. Conversely, if f is quasi-finite at x, and if also, the local ring of x in the fiber f < sup >− 1 </ sup >( f ( x )), is a field and a finite separable extension of κ ( f ( x )), then f is unramified at x .< ref > EGA IV < sub > 4 </ sub >, Théorème 17. 4. 1 .</ ref >
Conversely, every distributive lattice is isomorphic to a ring of sets ; in the case of finite distributive lattices, this is Birkhoff's representation theorem and the sets may be taken as the lower sets of a partially ordered set.
Conversely and can
Conversely, in the English language as a whole, singular verb forms can often be used with nouns ending in "- s " that were once considered plural ( for example: " Physics is my favorite academic subject ").
Conversely, non-spontaneous electrochemical reactions can be driven forward by the application of a current at sufficient voltage.
Conversely, badly managed food aid can create problems by disrupting local markets, depressing crop prices, and discouraging food production.
Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).
Conversely, rifle bullets can pierce light armor and are easier to shoot accurately, but even a carbine such as the Colt M4 is larger and / or longer than a submachine gun, making it harder to maneuver in close quarters.
Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces ( such as electromagnetism or friction ), can be used to define the geometry of space, as well as a time coordinate.
Conversely, a high pH, low CO < sub > 2 </ sub >, or low 2, 3 BPG favors the relaxed form which can better bind oxygen.
Conversely, a very severe bit, in the right hands, can transmit subtle commands that cause no pain to the horse.
Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.
Conversely, every formally real field can be equipped with a compatible total order, that will turn it into an ordered field.
Conversely we have a b if and only if a < b or a ~ b. This is the reason for using the notation ""; "≤" can be confusing for a preorder that is not anti-symmetric, it may suggest that a ≤ b implies that a < b or a
Conversely, the interior of the box has a constant, zero potential energy .< ref > Actually, any constant, finite potential can be specified within the box.
Conversely, though every president from Washington to John Quincy Adams can be definitely assigned membership in an Anglican or Unitarian body, the significance of these affiliations is often downplayed as unrepresentative of their true beliefs.
Conversely, extremely thin jewelry can cause the same tearing in what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing, especially if the thin jewelry bears any weight.
Conversely, specifying the symmetry can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it ; this is one way of looking at the Erlangen programme.
Conversely, water deep in the ocean near geothermal vents can reach temperatures of hundreds of degrees and remain liquid.
Conversely, AES is sensitive to the lighter elements, and unlike X-ray fluorescence, Auger peaks can be detected for elements as light as lithium ( Z = 3 ).