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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.

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## 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 ).

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