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Conversely, if this identity holds in a ring R for all pairs of elements a and b of the ring, then R is commutative.

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## Some Related Sentences

Conversely and if

__Conversely__

**,**

__if__statistics were uncovered which contradicted

**a**cherished theory

**,**

**the**sources were denounced as faulty

**.**

__Conversely__

**,**experimenters would consider as impressive such statements as

**the**following

**,**which

**,**

__if__they turned out to be hits

**,**are so unusual as to be really significant:

__Conversely__

**,**

__if__he gives

**a**heavy rating to his own reading

**,**

**and**finds more accurate facts

**in**it than

**in**

**the**others

**,**

**a**point

**is**chalked up

**for**

**the**intrinsic

**,**objective meaningfulness

**of**

**this**type

**of**mediumistic material

**.**

__Conversely__

**,**

**a**subset

**R**defines

**a**binary function

__if__

**and**only

__if__

**,**

**for**any x

**in**X

**and**y

**in**Y

**,**there exists

**a**unique z

**in**Z such that ( x

**,**y

**,**z ) belongs to

**R**

**.**

__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

**.**

__Conversely__

**,**

__if__

**the**second theory

**is**correct

**,**

**then**

**the**Athenians were merely reacting to

**the**Persians attacking them

**.**

__Conversely__

**the**equilibrium position

**is**said to be " far to

**the**left "

__if__hardly any product

**is**formed from

**the**reactants

**.**

__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__

**,**

__if__

**the**amount

**of**fat

**is**increased

**,**increasing

**the**number

**of**calories ingested will only add weight

**.**

__Conversely__

**,**

__if__

**the**source

**of**waves

**is**moving away from

**the**observer

**,**each wave

**is**emitted from

**a**position farther from

**the**observer than

**the**previous wave

**,**so

**the**arrival time between successive waves

**is**increased

**,**reducing

**the**frequency

**.**

__Conversely__every partition

**of**comes from an equivalence relation

**in**

**this**way

**,**according to which

__if__

**and**only

__if__

**and**belong to

**the**same set

**of**

**the**partition

**.**

If neither A nor B includes

**the**idea**of**existence**,****then**" some A are B " simply adjoins A to B**.**__Conversely__**,**__if__A or B do include**the**idea**of**existence**in****the**way that " triangle " contains**the**idea " three angles equal to two right angles ",**then**" A exists "**is**automatically true**,****and**we have an ontological proof**of**A's existence**.**__Conversely__

**,**

__if__

**the**measured potential

**is**negative

**,**

**the**electrode

**is**more oxidizing than

**the**SHE ( such as Zn

**in**ZnSO < sub > 4 </ sub > where

**the**standard electrode potential

**is**− 0

**.**76 V ).

__Conversely__

**,**

__if__

**the**firm

**is**able to get bulk discounts

**of**an input

**,**

**then**it could have economies

**of**scale

**in**some range

**of**output levels even

__if__it has decreasing returns

**in**production

**in**that output range

**.**

__Conversely__

**,**daylight stock shot

**in**daylight will look normal

**,**but orange

__if__shot under tungsten lights

**.**

__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 and identity

__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__

**,**

**if**( A

**,**m

**,**e

**,**inv )

**is**

**a**group object

**in**one

**of**those categories

**,**

**then**m necessarily coincides with

**the**given operation on A

**,**e

**is**

**the**inclusion

**of**

**the**given

__identity__element on A

**,**inv

**is**

**the**inversion operation

**and**A with

**the**given operation

**is**an abelian group

**.**

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__

**,**retaining

**a**series ' original title sequence can allow

**a**producer to change many key

**elements**within

**a**programme itself

**,**without losing

**the**show's on-screen

__identity__

**.**

__Conversely__

**,**Western sources erroneously define

**the**" Persian " " ethnicity " as basically anyone living

**in**Iran who does not claim

**a**secondary regional linguistic

__identity__

**.**

__Conversely__

**,**placeholders can be used to conceal

__identity__

**,**as seen

**in**

**the**above Gilbert

**and**Sullivan lyrics

**.**

__Conversely__

**,**given any Lie algebra with

**a**direct sum decomposition satisfying these three conditions

**,**

**the**linear map σ

**,**equal to

**the**

__identity__on

**and**minus

**the**

__identity__on

**,**

**is**an involutive automorphism

**.**

__Conversely__

**,**

**the**individual claiming an attribute may only grant selective access to its information

**,**e

**.**g

**.**when one proves

__identity__

**in**

**a**bar or paypal authentication

**for**payment at

**a**web site

**.**

Conversely and holds

__Conversely__

**,**externalism

__holds__that it

**is**things about

**the**world which motivate us

**,**justify our beliefs

**,**determine meaning

**,**etc

**.**

__Conversely__

**,**simply having negative relationships with some women does not necessarily mean someone

__holds__misogynistic views

**.**

__Conversely__

**,**

**the**following characterization

**of**derived functors

__holds__: given

**a**family

**of**functors

**R**< sup > i </ sup >: A → B

**,**satisfying

**the**above

**,**i

**.**e

**.**mapping short exact sequences to long exact sequences

**,**such that

**for**every injective object I

**of**A

**,**

**R**< sup > i </ sup >( I )= 0

**for**every positive i

**,**

**then**these functors are

**the**right derived functors

**of**

**R**< sup > 0 </ sup >.

If f

**is**flat**,****then**.< ref > EGA IV < sub > 2 </ sub >, Corollaire 6**.**1**.**2 .</ ref >__Conversely__**,****if****this**equality__holds__**for****all**x**,**X**is**Cohen-Macaulay**,****and**Y**is**regular**,****then**f**is**flat .< ref > EGA IV < sub > 2 </ sub >, Proposition 6**.**1**.**5**.**__Conversely__

**,**

**a**business can have negative net assets showing on its balance sheet but still be cash-flow solvent

**if**ongoing revenue

**is**able to meet debt obligations

**,**

**and**thus avoid default:

**for**instance

**,**

**if**it

__holds__long term debt

**.**

Conversely and ring

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 ).__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__

**,**

**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

**.**

__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

**.**

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